Chapter 9: Q21. (page 566)

Solve the equation by completing the square. Round to the nearest tenth.
$2 x^{2} + 4 x - 5 = 7$

Short Answer

Expert verified

$x = - 3.6, 1.6$ 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 perfect square a+b2.

${(a + b)}^{2} = a^{2} + 2 a b + b^{2} ........... (1)$

Step 3. Solve the equation 2x2+4x−5=7 by completing the square.

Use (1) to solve the equation.

$2 x^{2} + 4 x - 5 = 7 2 x^{2} + 4 x = 7 + 5 2 (x^{2} + 2 x) = 12 x^{2} + 2 x = \frac{12}{2} x^{2} + 2 x = 6$

$x^{2} + 2 (x) (1) = 6 x^{2} + 2 (x) (1) + 1^{2} = 6 + 1^{2} {(x + 1)}^{2} = 6 + 1 {(x + 1)}^{2} = 7 x + 1 = \pm \sqrt{7} x = - 1 \pm \sqrt{7}$

Use calculator.

$\begin{array}{l} x = - 3.645751311, 1.645751311 \\ x ≃ - 3.6, 1.6 \end{array}$

Hence, $x = - 3.6, 1.6$ are the solutions of the given equation.

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Solve the equation by completing the square. Round to the nearest tenth.
$2 x^{2} + 4 x - 5 = 7$

Short Answer

Step by step solution

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

Step 2. Define the perfect square a+b2.

Step 3. Solve the equation 2x2+4x−5=7 by completing the square.

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Solve the equation by completing the square. Round to the nearest tenth.2x2+4x−5=7

Short Answer

Step by step solution

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

Step 2. Define the perfect square a+b2.

Step 3. Solve the equation 2x2+4x−5=7 by completing the square.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Pure Maths

Applied Mathematics

Calculus

Decision Maths

Statistics

Study anywhere. Anytime. Across all devices.

Solve the equation by completing the square. Round to the nearest tenth.
$2 x^{2} + 4 x - 5 = 7$