solve x2=20+8x
2=20+8x |-20
-18=8x | /8
-18/8=x
x^2 - 8x - 20 = 0
(x-10)(x+2) = 0
...
To solve the equation x^2 = 20 + 8x, we can rearrange it into a quadratic equation:
x^2 - 8x - 20 = 0
Now, we can apply the quadratic formula to find the values of x that satisfy this equation. The quadratic formula states:
x = (-b ± √(b^2 - 4ac)) / (2a)
In the given quadratic equation, a = 1, b = -8, and c = -20. Plugging these values into the quadratic formula, we get:
x = (8 ± √((-8)^2 - 4(1)(-20))) / (2*1)
Simplifying further:
x = (8 ± √(64 + 80)) / 2
x = (8 ± √144) / 2
Now, we can calculate the values of x:
x₁ = (8 + √144) / 2
x₂ = (8 - √144) / 2
x₁ = (8 + 12) / 2
x₂ = (8 - 12) / 2
x₁ = 20 / 2
x₂ = -4 / 2
x₁ = 10
x₂ = -2
Therefore, the solutions to the quadratic equation x^2 = 20 + 8x are x = 10 and x = -2.