Question

Rewrite the equation x² + 28x+ 193.5 = 0 in the form (x-p)² = q

Answer 1

To rewrite the quadratic equation in a specific form, we need to complete the square.

Step-by-step explanation:

To rewrite the equation x² + 28x+ 193.5 = 0 in the form (x-p)² = q, we need to complete the square. Here's the step-by-step process:

1. Move the constant term to the other side of the equation: x² + 28x = -193.5
2. Divide both sides of the equation by the coefficient of x² (which is 1): x² + 28x = -193.5
3. Take half the coefficient of x (which is 28), square it (which is 784), and add it to both sides of the equation: x² + 28x + 784 = -193.5 + 784
4. Factor the perfect square on the left side of the equation: (x + 14)² = 590.5

Therefore, the equation x² + 28x+ 193.5 = 0 can be rewritten in the form (x+14)² = 590.5.