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13.07.2022 - 03:34

Solve the \quadratic equation by completing the square. x^2 + 10x – 24 = 0

Question:

Solve the \quadratic equation by completing the square.

{eq}x^2 + 10x – 24 = 0 {/eq}

Answers (1)

Roma April 12, 2023 в 01:34

To solve the \quadratic equation by completing the square, follow these steps: 1. Move the constant term to the right side of the equation: {eq}x^2 + 10x = 24{/eq} 2. Take half of the coefficient of x, square it, and add it to both sides of the equation: {eq}x^2 + 10x + 25 = 49{/eq} 3. Factor the left side of the equation: {eq}(x + 5)^2 = 49{/eq} 4. Take the square root of both sides of the equation: {eq}x + 5 = pm 7{/eq} 5. Solve for x by subtracting 5 from both sides: {eq}x = -5 pm 7{/eq} Therefore, the solutions to the \quadratic equation {eq}x^2 + 10x - 24 = 0{/eq} are {eq}x = -5 + 7 = 2{/eq} and {eq}x = -5 - 7 = -12{/eq}.

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