Question

Rewrite the equation in the form (x-p)² = q.
2
x +0.2x - 19.4=0

Answer 1

To rewrite the given quadratic equation in the form (x-p)² = q, you complete the square by dividing the linear coefficient by 2, squaring it, adding it to both sides, and rearranging. The result is (x + 0.05)² = 9.7025.

Step-by-step explanation:

To rewrite the equation 2x² + 0.2x - 19.4 = 0 in the form (x - p)² = q, we first need to complete the square. The quadratic equation has the form ax² + bx + c = 0, where a, b, and c are constants.

Let's divide the entire equation by 2 to simplify it:

x² + 0.1x - 9.7 = 0

Here's a step-by-step process to complete the square:

1. Move the constant term to the other side of the equation: x² + 0.1x = 9.7.
2. Divide the coefficient of x by 2, and then square it: (0.1 / 2)² = 0.0025.
3. Add this number to both sides of the equation: x² + 0.1x + 0.0025 = 9.7 + 0.0025.
4. Write the left side as a square: (x + 0.05)² = 9.7025.
5. Therefore, in the form (x - p)² = q, we have: (x + 0.05)² = 9.7025.

In this completed form, p is -0.05 and q is 9.7025.