Question

Solve for x (x-5)^2= 2x^2-19x+39. If there is more than one solution, separate them with commas. \

Answer 1

To solve the quadratic equation (x-5)^2= 2x^2-19x+39, we expand the left side, rearrange the equation to set it to zero, simplify it, and then factor it to find that the solutions are x = -7 and x = -2.

Step-by-step explanation:

To solve the equation (x-5)^2= 2x^2-19x+39, we first expand and simplify the left side of the equation:

• (x-5)(x-5) = x^2 - 10x + 25

Now we have the equation:

x^2 - 10x + 25 = 2x^2 - 19x + 39

Next, we rearrange this equation to set it to zero:

• x^2 - 2x^2 + 10x - 19x + 25 - 39 = 0
• -x^2 - 9x - 14 = 0

We then multiply through by -1 to make the x^2 term positive:

• x^2 + 9x + 14 = 0

This is a quadratic equation, and we can solve for x by factoring:

• (x + 7)(x + 2) = 0

Setting each factor equal to zero gives us the solutions:

• x + 7 = 0 → x = -7
• x + 2 = 0 → x = -2

Therefore, the solutions for the equation are x = -7, -2.