Solve the equation by completing the square. If necessary, round to the nearest hundredth.
Let's solve the equation by completing the square:
x^2 + 6x - 8 = 0
First, we need to move the constant term to the other side:
x^2 + 6x = 8
Next, we need to find the value that we add and subtract to complete the square. To do this, we take half of the coefficient of x (6) and square it:
(6/2)^2 = 9
Now, add and subtract 9 within the equation:
x^2 + 6x + 9 = 8 + 9
(x + 3)^2 = 17
Now we have the equation in the form (x + h)^2 = k. Taking the square root of both sides gives us:
x + 3 = ±√17
x = -3 ± √17
Therefore, the solutions to the equation are x = -3 ± √17. Rounded to the nearest hundredth, the solutions are:
x = -3 + √17 ≈ 1.12
x = -3 - √17 ≈ -7.12
So, the solutions to the equation x^2 + 6x - 8 = 0 are approximately 1.12 and -7.12.