SOLUTION: show me how to solve this equation 2(x-8)^ 2+x^2=x(x=51)-43x

Question 548842: show me how to solve this equation 2(x-8)^ 2+x^2=x(x=51)-43x
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
2*(x-8)^2 +x^2 = x*(x-51) - 43*x
.
Use FOIL to expand the second term.
.
2*(x^2-16x+64) +x^2 = x*(x-51) - 43*x
.
Use the distributive property to eliminate the parentheses.
.
2x^2 -32x + 128 +x^2 = x^2 -51x - 43x
.
Collect terms
.
3x^2 -32x + 128 = x^2 -94x
.
Subtract x^2 from both sides
.
2x^2 -32x + 128 = -94x
.
Add 94x to both sides
.
2x^2 +62x + 128 = 0
.
Divide both sides by 2
.
x^2 +31x + 64 = 0
.

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=705 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -2.22408195264825, -28.7759180473518. Here's your graph:

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