Question

Solve for x square root of 8-2x=x

Answer 1

To solve the equation √(8-2x) = x, square both sides to eliminate the square root, rearrange into a quadratic form, factor, and solve for x to find that x can be either -4 or 2.

Step-by-step explanation:

To solve the equation sqrt(8-2x) = x, we can follow these steps:

1. Square both sides of the equation to eliminate the square root: (sqrt(8-2x))^2 = x^2
2. Simplify the equation: 8-2x = x^2
3. Rearrange the equation into a quadratic form: x^2 + 2x - 8 = 0
4. Factor the quadratic equation: (x+4)(x-2) = 0
5. Solve for x by setting each factor equal to zero: x+4 = 0 or x-2 = 0
6. Find the values of x: x = -4 or x = 2

So, the solutions to the equation are x = -4 and x = 2.