solve the equation by completing the square x^2+10x=18
To solve the equation by completing the square, follow these steps:
1. Rearrange the equation so that the constant term is on the right side:
x^2 + 10x = 18
2. To complete the square, take half of the coefficient of x (which is 10) and square it:
(10/2)^2 = 25
3. Add this to both sides of the equation:
x^2 + 10x + 25 = 18 + 25
x^2 + 10x + 25 = 43
4. Rewrite the left side as a squared binomial:
(x + 5)^2 = 43
5. Take the square root of both sides to solve for x:
x + 5 = ±√43
x = -5 ±√43
Therefore, the solutions to the equation x^2 + 10x = 18 are x = -5 + √43 and x = -5 - √43.