Question

Solve the equation for all values of x by completing the square. 5x²-50x=-60

Answer 1

To solve the equation 5x²-50x=-60 by completing the square, divide the entire equation by 5, move the constant term to the right side of the equation, add the square of half the coefficient of x to both sides, simplify, and take the square root to find two solutions for x.

Step-by-step explanation:

To solve the equation 5x²-50x=-60 by completing the square, follow these steps:

1. Make sure the coefficient of x² is 1. Divide the entire equation by 5 to get x²-10x=-12.
2. Move the constant term (-12) to the right side of the equation to create space for completing the square: x²-10x+__=-12+__.
3. Take half of the coefficient of x (-10/2=-5) and square it to get 25. Add 25 to both sides of the equation: x²-10x+25=-12+25.
4. The left side of the equation is now a perfect square: (x-5)²=-12+25.
5. Simplify the right side of the equation to get (x-5)²=13.
6. Take the square root of both sides to solve for x: x-5=sqrt(13) or x-5=-sqrt(13).
7. Add 5 to both sides of each equation to find the values of x: x=5+sqrt(13) or x=5-sqrt(13).