solve the equation x^2-6x=-8

Answer 1

To solve the equation x^2 - 6x = -8, we need to first set the equation equal to zero:

x^2 - 6x + 8 = 0

Now, we need to factor the equation or use the quadratic formula to solve for x.

Since our equation is in the form ax^2 + bx + c = 0, we need to find two numbers that multiply to a*c (in this case, 2*8 = 16) and add up to b (in this case, -6). The two numbers that fit those criteria are -2 and -4.

So, we can rewrite the equation as:

x^2 - 2x - 4x + 8 = 0
(x^2 - 2x) + (-4x + 8) = 0
x(x - 2) - 4(x - 2) = 0
(x - 2)(x - 4) = 0

Now, we set each factor to zero:

x - 2 = 0 or x - 4 = 0

So, x = 2 or x = 4

Therefore, the solutions to the equation x^2 - 6x = -8 are x = 2 and x = 4.