Question

Find the value that completes the square and then rewrite it as a perfect square.

A) -361
B) -144
C) +361
D) +144

Answer 1

To complete the square in the given equation, we divide the coefficient of x by 2, square it, and add and subtract this value to the equation. The value that completes the square is 0.0001113025, which can be rewritten as a perfect square by adding it to the equation. The perfect square form of the equation is (x + 0.01055)² = 0.0001113025.

Step-by-step explanation:

In this case, we have the equation x² + 0.0211x - 0.0211 = 0. To complete the square, we divide the coefficient of x by 2 and square it, then add and subtract this value to the equation.

Dividing 0.0211 by 2 gives us 0.01055. Squaring this value gives us 0.0001113025.

Therefore, the value that completes the square is 0.0001113025. To rewrite it as a perfect square, we add it to the equation:

x² + 0.0211x - 0.0211 + 0.0001113025 = 0.0001113025

We can simplify this further:

x² + 0.0211x + 0.0001113025 = 0.0001113025

Now, the equation is a perfect square: (x + 0.01055)² = 0.0001113025.