Question

Solve by completing the square. f² + 4f - 43 = 0. Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth. f = ____ or f = ____

Answer 1

To solve the quadratic equation f² + 4f - 43 = 0 by completing the square, we rearrange the terms, complete the square, and then take the square root, ultimately finding that f = 4.86 or f = -8.86 when the square root is calculated and rounded to the nearest hundredth.

Step-by-step explanation:

To solve the equation f² + 4f - 43 = 0 by completing the square, follow these steps:

1. Move the constant term to the right side of the equation: f² + 4f = 43.
2. Divide the coefficient of the f term by 2 and square it: (4/2)² = 4.
3. Add 4 to both sides of the equation to complete the square: f² + 4f + 4 = 47.
4. Write the left side as a squared binomial: (f + 2)² = 47.
5. Take the square root of both sides: f + 2 = ±√47.
6. Subtract 2 from both sides to solve for f: f = -2 ±√47.

The solutions are not rational numbers and can't be simplified to integers or fractions. Therefore, we need to express the square root as decimals rounded to the nearest hundredth: f = -2 ± 6.86, which gives us f = 4.86 or f = -8.86.