Chapter 9: Q23. (page 566)

Solve the equation by completing the square. Round to the nearest tenth.
$x^{2} - 10 x = - 24$

Short Answer

Expert verified

$x = 4, 6$ are the solutions of the given equation.

Step by step solution

Step 1. Define the standard form of the quadratic equation.

A quadratic equation, which is written in the form, $a x^{2} + b x + c = 0$ , where, $a \neq 0$ is called the standard form of the quadratic equation.

Step 2. Define the quadratic formula.

For the quadratic equation $a x^{2} + b x + c = 0,$ where, $a \neq 0$ is given by

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

Step 3. Solve the equation x2−10x=−24 by completing the square.

Change the equation $x^{2} - 10 x = - 24$ in standard form.

The standard form is

$x^{2} - 10 x + 24 = 0$

Compare the quadratic equation $x^{2} - 10 x + 24 = 0$ with the quadratic equation $a x^{2} + b x + c = 0$ .

$a = 1, b = - 10, c = 24$

Substitute, $a = 1, b = - 10$ and $c = 24$ in $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ .

$x = \frac{- (- 10) \pm \sqrt{{(- 10)}^{2} - 4 (1) (24)}}{2 (1)} x = \frac{10 \pm \sqrt{100 - 96}}{2} x = \frac{10 \pm \sqrt{4}}{2} x = \frac{10 \pm 2}{2} x = \frac{10 - 2}{2}, \frac{10 + 2}{2} x = \frac{8}{2}, \frac{12}{2} x = 4, 6$

Hence, $x = 4, 6$ are the solutions of the given equation.

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Solve the equation by completing the square. Round to the nearest tenth.
$x^{2} - 10 x = - 24$

Short Answer

Step by step solution

Step 1. Define the standard form of the quadratic equation.

Step 2. Define the quadratic formula.

Step 3. Solve the equation x2−10x=−24 by completing the square.

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Solve the equation by completing the square. Round to the nearest tenth.x2−10x=−24

Short Answer

Step by step solution

Step 1. Define the standard form of the quadratic equation.

Step 2. Define the quadratic formula.

Step 3. Solve the equation x2−10x=−24 by completing the square.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Probability and Statistics

Calculus

Theoretical and Mathematical Physics

Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Solve the equation by completing the square. Round to the nearest tenth.
$x^{2} - 10 x = - 24$