Question

Solve the equation –232 + 10– 2 = 0 by completing the square. Select all of the true statements:

A. The roots are r = 5 + √21.
B. The roots are r = 5 + √0.
C. The roots are r = -5 ± √2.
D. The axis of symmetry is x = 5.
E. The axis of symmetry is x = -5.
F. The axis of symmetry is y = 2.
G. I added 2 to both sides of the equation to complete the square.
H. I added 5 to both sides of the equation to complete the square.

Answer 1

To solve the equation -232 + 10^-2 = 0 by completing the square, first isolate the variable by subtracting -232 from both sides. Then, add the square of half the coefficient of x to both sides to complete the square. Finally, solve for x by taking the square root of both sides.

Step-by-step explanation:

To solve the equation -232 + 10^-2 = 0 by completing the square, we first need to isolate the variable. We can do this by subtracting -232 from both sides of the equation, resulting in 10^-2 = 232.

Now, let's complete the square.

Adding the square of half the coefficient of x to both sides of the equation, we get (10^-2) + (1/2)^2 = 232 + (1/2)^2. This simplifies to (10^-2) + 1/4 = 232 + 1/4, or 10^-2 + 1/4 = 929/4.

Now, we can rewrite the left side of the equation as a perfect square: (10^-1 + 1/2)^2 = (929/4).

Taking the square root of both sides, we get 10^-1 + 1/2 = ± √(929/4), which simplifies to 5 + √(929/4) or 5 - √(929/4).