+0  
 
0
1
2
avatar+1712 

Find all solutions to the equation $x^2 - 11x - 42 = -2x + 10 - x^2 - 5x + 16$.

 Jun 9, 2024

Best Answer 

 #2
avatar+74 
+1

Sorry, I've just noticed an error with my answer. The starting equation should simplify to 2x^2 - 4x - 68. You can use the same process to find out that the roots are 1 + sqrt(35) and 1 - sqrt(35)

 

Full process:

\(2x^2-4x-68=0\)

\(x^2-2x-34=0\)

\(x^2-2x+1=35\)

\((x-1)^2 = 35\)

\(x-1 = \pm \sqrt{35}\)

\(x = 1 \pm \sqrt{35}\)

 Jun 9, 2024
 #1
avatar+74 
0

We can first simplify this equation by combining like terms

\(x^2+x^2-11x+2x+5x-42-10-16 = 0\)

\(2x^2+4x-68 = 0\)

\(x^2+4x-34=0\)

Now we can use completing the square to solve this polynomial equation.

\(x^2+4x -34 + 38 = 0 + 38\)

\(x^2+4x+4 = 38\)

\((x+2)^2 = 38\)

\(x + 2 = \pm \sqrt{38}\)

\(x = -2 \pm \sqrt{38}\)

So the 2 solutions are -2 + sqrt(38) and -2 - sqrt(38)

 Jun 9, 2024
 #2
avatar+74 
+1
Best Answer

Sorry, I've just noticed an error with my answer. The starting equation should simplify to 2x^2 - 4x - 68. You can use the same process to find out that the roots are 1 + sqrt(35) and 1 - sqrt(35)

 

Full process:

\(2x^2-4x-68=0\)

\(x^2-2x-34=0\)

\(x^2-2x+1=35\)

\((x-1)^2 = 35\)

\(x-1 = \pm \sqrt{35}\)

\(x = 1 \pm \sqrt{35}\)

Maxematics  Jun 9, 2024

1 Online Users

avatar