Question

Rewrite the equation [x² + 3x - 28 = 0] by completing the square.

Answer 1

The completed square form is (x + 1.5)² = 30.25.

Step-by-step explanation:

To rewrite the equation x² + 3x - 28 = 0 by completing the square, we first move the constant term to the other side of the equation, leaving the x² and x terms on one side.

Here's the step-by-step process:

1. x² + 3x = 28
2. Now find the number that completes the square for the x terms. This is done by taking half of the coefficient of x, squaring it, and adding it to both sides of the equation. Half of 3 is 1.5, and 1.5² is 2.25.
3. Add 2.25 to both sides: x² + 3x + 2.25 = 28 + 2.25
4. The equation now becomes (x + 1.5)² = 30.25

Now you have a perfect square on one side of the equation, making it easier to solve for x by taking the square root of both sides.