Question

Slove each equation by completing the square x^2 + 12x - 1 =3

Answer 1

To solve the equation x^2 + 12x - 1 = 3 by completing the square, add 36 to both sides to form a perfect square, take the square root of both sides, and solve for x resulting in x = -6 ±√40.

Step-by-step explanation:

To solve the equation x^2 + 12x - 1 = 3 by completing the square, follow these steps:

1. Move the constant term to the right side of the equation: x^2 + 12x = 4.
2. Divide the coefficient of x by 2 and square the result to find the number that completes the square: (12/2)^2 = 36.
3. Add this number to both sides of the equation to maintain equality: x^2 + 12x + 36 = 40.
4. Now the left side of the equation forms a perfect square: (x + 6)^2 = 40.
5. Take the square root of both sides, remembering to consider both the positive and negative square roots: x + 6 = ±√40.
6. Solve for x by subtracting 6 from both sides: x = -6 ±√40.

Finally, simplify the square root (if possible) and express the answer in simplest radical form or as a decimal.