Solve the equation by completing the square. Round to the nearest hundredth if necessary.
x^2 - x - 7 = 0
To complete the square for the given equation, we need to rewrite it in the form (x - h)^2 = k.
First, move the constant term to the right side of the equation:
x^2 - x = 7
To find the value of h, take the coefficient of x, divide it by 2, and then square it: (1/2)^2 = 1/4.
Add 1/4 to both sides of the equation to complete the square:
x^2 - x + 1/4 = 7 + 1/4
Combine like terms:
(x - 1/2)^2 = 29/4
Take the square root of both sides:
x - 1/2 = ± √(29/4)
Rationalize the denominator:
x - 1/2 = ± √(29)/2
Add 1/2 to both sides to isolate x:
x = 1/2 ± √(29)/2
Therefore, the solution to the equation x^2 - x - 7 = 0 is x = 1/2 ± √(29)/2. We can round this to the nearest hundredth:
x ≈ 1.79 or x ≈ -0.79