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I don't know if this explains why but... it's because the answer has separate solutions, the two solutions can be written as \({(8y-11)^2}=169 \\ \downarrow Square-root \space both \space of \\ the \space equation \\ 8y-11=±13 \\ \downarrow Separate \space the \space solutions \\ 8y-11=13 \\ or \\ 8y-11=-13 \)

and this is why there are two answers.

Or you could simply say

8y - 11 = 13   and   8y - 11 = -13   are the two possibilities

From one you get y = (13 + 11)/8 → 3

From the other you get y = (-13 + 11)/8 → -1/4

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There are an infinite number of solutions as you can see from the following:

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a, b, c means the coefficient of x², x¹, and x⁰ respectively.

Example: In \(x^2 - x + 1\) , a = 1, b = -1, c = 1.

In \(7x^2 - 22x + 15\), a = 7, b = -22, c = 15.

\(\boxed{ \dfrac{a}{b}-\dfrac{x}{y} = \dfrac{ay - bx}{by}}\)

\(\dfrac{5}{14}-\dfrac{2}{221}\\ =\dfrac{5 \times 221-14\times 2}{14\times 221}\\ =\dfrac{1105 - 28}{3094}\\ =\dfrac{1077}{3094}\\ \)

It's the simplest form already, no need to simplify.

0.23 x 13 = 2.99 m <--- That's really long!!

\((8x^3 - 2)(x^3 -7)\\ = 8x^6 - 2x^3 - 56x^3 + 14\\ = 8x^6 - 58x^3 + 14\)

\((8y-11)^2 = 169\\ 64y^2 - 176y + 121 = 169\\ 64y^2 - 176y -48 = 0\\ 16y^2 - 44y - 12 = 0\\ 4y^2 - 11y - 3 = 0\\ (y-3)(4y+1) = 0\\ y = 3 \text{ or }y = -\dfrac{1}{4}\)

I think what you have done is just taking square roots for both sides, but this method cannot always give all the answers to a polynomial equation.(including quadratics)

I found all this on google and wikipedia

A binomial is an algebraic expression of the sum or the difference of two terms also 

In mathematics:

Binomial (polynomial), a polynomial with two terms

Binomial coefficient, numbers appearing in the expansions of powers of binomials

Binomial QMF, a perfect-reconstruction orthogonal wavelet decomposition

Binomial theorem, a theorem about powers of binomials

Binomial type, a property of sequences of polynomials

In probability and statistics:

Binomial distribution, a type of probability distribution

Binomial test, a test of significance

In computing science:

Binomial heap, a data structure

In linguistics:

Binomial pair, a sequence of two or more words or phrases in the same grammatical category, having some semantic relationship and joined by some syntactic device

In biology:

Binomial nomenclature, a Latin two-term name for a species, such as Sequoia sempervirens

In finance:

Binomial options pricing model, a numerical method for the valuation of options

 How do you come to get this long form? I KNOW the answer to this equation is 40213 (When the available numbers are 0,1,2,3,4) but I don't understand the long form of this equation. 

How do i solve this equation?

5x/6 - 3/8 = 11/24 + 5x/12

\(\begin{array}{|rcll|} \hline x\cdot\frac56 - \frac38 &=& \frac{11}{24} + x\cdot\frac{5}{12} \qquad &| \qquad \cdot 12\\\\ x\cdot\frac56 \cdot 12 - \frac38 \cdot 12 &=& \frac{11}{24} \cdot 12 + x\cdot\frac{5}{12} \cdot 12\\\\ x\cdot 5 \cdot 2 - 3\cdot \frac{12}{8} &=& \frac{11}{2} + x\cdot 5\\\\ 10x- 3\cdot \frac{3}{2} &=& \frac{11}{2} + 5x \\\\ 10x - \frac{9}{2} &=& \frac{11}{2} + 5x \qquad &| \qquad -5x\\\\ 10x -5x -\frac{9}{2} &=& \frac{11}{2} \qquad &| \qquad + \frac{9}{2}\\\\ 10x -5x &=& \frac{11}{2} + \frac{9}{2}\\\\ 5x &=& \frac{11+9}{2} \\\\ 5x &=& \frac{20}{2} \\\\ 5x &=& 10 \qquad &| \qquad : 5 \\\\ x &=& \frac{10}{5} \\\\ \mathbf{ x } & \mathbf{=} & \mathbf{2} \\ \hline \end{array}\)

finding x and y, what is 4x+10y and 11x+5y. both are equal to 90.

determinant method:

\(\begin{array}{|rcll|} \hline x &=& \frac{ \begin{vmatrix} 90 & 10\\90 & 5\end{vmatrix} } { \begin{vmatrix} 4 & 10\\11 & 5\end{vmatrix} } \\\\ &=& \frac{ 90\cdot \begin{vmatrix} 1 & 10\\1 & 5\end{vmatrix} } { 4\cdot 5 - 11 \cdot 10 } \\\\ &=& \frac{ -90\cdot \begin{vmatrix} 10 & 1\\5 & 1\end{vmatrix} } { -90 } \\\\ &=& \begin{vmatrix} 10 & 1\\5 & 1\end{vmatrix} \\\\ &=& 10-5 \\\\ &=& \mathbf{5} \\ \hline \end{array}\)

\(\begin{array}{|rcll|} \hline y &=& \frac{ \begin{vmatrix} 4 & 90\\11 & 90\end{vmatrix} } { \begin{vmatrix} 4 & 10\\11 & 5\end{vmatrix} } \\\\ &=& \frac{ 90\cdot \begin{vmatrix} 4 & 1\\11 & 1\end{vmatrix} } { 4\cdot 5 - 11 \cdot 10 } \\\\ &=& \frac{ -90\cdot \begin{vmatrix} 1 & 4\\1 & 11\end{vmatrix} } { -90 } \\\\ &=& \begin{vmatrix} 1 & 4\\1 & 11\end{vmatrix} \\\\ &=& 11-4 \\\\ &=& \mathbf{7} \\ \hline \end{array}\)

360 - 1/15 - 1/5 - 1/20 = ?

360 - 19/60 =359 41/60

40% off 91

40/100 x 91 =36.4

91 - 36.4 =54.60

Or

91 x 60/100 =54.60

how can u get 8 using 2, 4, and 7

2^(7-4) =2^3 = 8

cmon

43/50 =.86

Volume=4/3 x Pi x r^3

V=4/3 x 3.141592 x 8^3

V=2,144.66 cubic units.

Solve the following system:
{4 x+10 y = 90 | (equation 1)
11 x+5 y = 90 | (equation 2)
Swap equation 1 with equation 2:
{11 x+5 y = 90 | (equation 1)
4 x+10 y = 90 | (equation 2)
Subtract 4/11 × (equation 1) from equation 2:
{11 x+5 y = 90 | (equation 1)
0 x+(90 y)/11 = 630/11 | (equation 2)
Multiply equation 2 by 11/90:
{11 x+5 y = 90 | (equation 1)
0 x+y = 7 | (equation 2)
Subtract 5 × (equation 2) from equation 1:
{11 x+0 y = 55 | (equation 1)
0 x+y = 7 | (equation 2)
Divide equation 1 by 11:
{x+0 y = 5 | (equation 1)
0 x+y = 7 | (equation 2)
Collect results:
Answer: |x = 5                    and                    y = 7

Is your $2424 meant to be $24 and interest of 44% meant to be 4%???????? If yes, then you have:

$24 x 4/100 =$0.96 interest for 1 full year.

$0.96 x 35 years =$33.60 simple interest for 35 years.

$24.00 + $33.60 =$57.60 Balance in the account after 35 years.

There are a number of whole integer solutions, such as:

a=1, b= -1

a=2, b= -4

a=4, b= 8

a=5, b=5

a=6, b=4

a=9, b=3............etc.

A 8000 $

a= 0 and  b = 0 is one solution :) 

19^2+27^2-2(19)(27)*(cos(80)) = 911.836969713658

|x|<13

=-13 < x < 13