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# Pls help quadratic equation to standard form

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1.). (x-5)^2=(2x-3)^2

2.). (x+3)(x-4)=(x-2)^2

3.). 5x(6x-10)=-3x(7x-2)

Plssss help

Jun 22, 2017

#1
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1)

Solve for x:
(x - 5)^2 = (2 x - 3)^2

Take the square root of both sides:
x - 5 = 2 x - 3 or x - 5 = 3 - 2 x

Subtract 2 x - 5 from both sides:
-x = 2 or x - 5 = 3 - 2 x

Multiply both sides by -1:
x = -2 or x - 5 = 3 - 2 x

Add 2 x + 5 to both sides:
x = -2 or 3 x = 8

Divide both sides by 3:
Answer: | x = -2 or x = 8/3

2)

Solve for x:
(x - 4) (x + 3) = (x - 2)^2

Expand out terms of the left hand side:
x^2 - x - 12 = (x - 2)^2

Expand out terms of the right hand side:
x^2 - x - 12 = x^2 - 4 x + 4

Subtract x^2 - 4 x + 4 from both sides:
3 x - 16 = 0

Add 16 to both sides:
3 x = 16

Divide both sides by 3:
Answer: | x = 16/3

3)

Solve for x:
5 x (6 x - 10) = -3 x (7 x - 2)

Expand out terms of the left hand side:
30 x^2 - 50 x = -3 x (7 x - 2)

Expand out terms of the right hand side:
30 x^2 - 50 x = 6 x - 21 x^2

Subtract 6 x - 21 x^2 from both sides:
51 x^2 - 56 x = 0

Factor x from the left hand side:
x (51 x - 56) = 0

Split into two equations:
x = 0 or 51 x - 56 = 0

Add 56 to both sides:
x = 0 or 51 x = 56

Divide both sides by 51:
Answer: | x = 0           or          x = 56/51

Jun 22, 2017
#2
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1.). (x-5)^2=(2x-3)^2  simplify

(x - 5)  ( x - 5)  = (2x - 3) (2x - 3)   expand

x^2 - 10x  +  25  =  4x^2 - 12x + 9

0 = 3x^2  - 2x - 16    or

3x^2 - 2x  - 16  = 0

2.). (x+3)(x-4)=(x-2)^2  simplify

x^2 - x  - 12  =  (x -2) (x -2)

x^2 - x  -12   =  x^2   - 4x  + 4

3x - 16  = 0

3.). 5x(6x-10) = -3x(7x-2)   simplify

30x^2 -  50x  =  -21x^2 +  6x

51x^2 - 56x  = 0   Jun 22, 2017