Solve the equation by completing the square. Round to the nearest hundredth if necessary.
x² + 10x = 18
To solve this equation by completing the square, we first need to move the constant term to the other side of the equation:
x² + 10x = 18
x² + 10x - 18 = 0
Next, we need to complete the square by taking half of the coefficient of x, squaring it, and adding it to both sides of the equation:
x² + 10x + (10/2)² = 18 + (10/2)²
x² + 10x + 25 = 18 + 25
x² + 10x + 25 = 43
The left side of the equation can be factored into a perfect square:
(x + 5)² = 43
Taking the square root of both sides gives:
x + 5 = ±√43
x = -5 ±√43
Therefore, the solutions to the equation x² + 10x = 18 are approximately -8.93 and -1.07.