Solve x^2 -6x - 13 = 0 by completing the square. Give exact solutions.
A: x = ±√22 (or) x = ±4.69
(x - 3)^2 = 22
x - 3 =-+√(22)
3-√(22), 3+√(22)
The way my textbook gives:
x - 3 = -+√(22)
x = app. 7.7
x = app. -1.7
Thank you so much! Can you evaluate my other Algebra 1 posts as well?
To solve the quadratic equation x^2 - 6x - 13 = 0 by completing the square, follow these steps:
Step 1: Move the constant term to the right side of the equation:
x^2 - 6x = 13
Step 2: To complete the square, take half of the coefficient of x (which is -6) and square it:
(-6/2)^2 = 9
Step 3: Add the value obtained in step 2 to both sides of the equation:
x^2 - 6x + 9 = 13 + 9
x^2 - 6x + 9 = 22
Step 4: Express the left side of the equation as a perfect square:
(x - 3)^2 = 22
Step 5: Take the square root of both sides of the equation, remembering to consider both the positive and negative square roots:
√((x - 3)^2) = ±√22
x - 3 = ±√22
Step 6: Solve for x by adding 3 to both sides of the equation:
x = 3 ±√22
Therefore, the exact solutions to the quadratic equation x^2 - 6x - 13 = 0 by completing the square are x = 3 + √22 and x = 3 - √22.