Question

Solve the quadratic equation x²+3=-8x for all values of x by completing the square. What is the solution?

Answer 1

To solve the quadratic equation x² + 3 = -8x by completing the square, follow these steps: move terms to one side, add a perfect square trinomial, factor, solve for x.

Step-by-step explanation:

To solve the equation x² + 3 = -8x by completing the square, we need to follow these steps:

1. Move all terms to one side of the equation to get x² + 8x + 3 = 0.
2. Divide the coefficient of x by 2 and square the result. Add the squared result to both sides of the equation to make the left side a perfect square trinomial. By adding (8/2)^2 = 16 to both sides, the equation becomes x² + 8x + 16 + 3 = 16.
3. Factor the left side of the equation, which becomes (x + 4)² + 3 = 16.
4. Subtract 3 from both sides of the equation to get (x + 4)² = 13.
5. Take the square root of both sides to eliminate the square on the left side. The two possible solutions are x + 4 = √13 and x + 4 = -√13.
6. Solve for x by subtracting 4 from both sides. The final solutions are x = √13 - 4 and x = -√13 - 4.