Solve x² - 2x - 24 = 0, for x, by completing the square.

x² - 2x - 24 = 0

x² - 2x = 24 {added 24 to each side}

x² - 2x + 1 = 24 + 1 {took half of the coefficient of x, squared it, and added it to each side}

(x - 1)² = 25 {wrote the left side as the square of a binomial, added 24 and 1 on the right}

x - 1 = ±√25 {took the square root of each side}

x - 1 = ±5 {evaluated the square root of 25 to be 5}

x = 1 ± 5 {added 1 to each side}

x = 1 + 5 or x = 1 - 5 {split using the ± sign}

6 and -4 are the x-intercepts in the graph of the parabola, as shown below.

x² - 2x = 24 {added 24 to each side}

x² - 2x + 1 = 24 + 1 {took half of the coefficient of x, squared it, and added it to each side}

(x - 1)² = 25 {wrote the left side as the square of a binomial, added 24 and 1 on the right}

x - 1 = ±√25 {took the square root of each side}

x - 1 = ±5 {evaluated the square root of 25 to be 5}

x = 1 ± 5 {added 1 to each side}

x = 1 + 5 or x = 1 - 5 {split using the ± sign}

**x = 6 or -4**6 and -4 are the x-intercepts in the graph of the parabola, as shown below.

**- Algebra House**