Chapter 10: Q 81 (page 1181)

Solve the equation by completing square method.
$a^{2} - 10 a = - 5$

Short Answer

Expert verified

The solutions are $a = 5 + 2 \sqrt{5}, a = 5 - 2 \sqrt{5}$ .

Step by step solution

Given Information

The Given equation is $a^{2} - 10 a = - 5$ .

Isolate the variable terms on one side and the constant terms on the other.

The variable terms are on the left side.

$a^{2} - 10 a = - 5$

Here, $b = - 10$

Find 12b2

$= {(\frac{1}{2} (- 10))}^{2} = {(- 5)}^{2} = 25$

Add $25$ to both sides of equation.

$a^{2} - 10 + 25 = - 5 + 25 a^{2} - 10 a + 25 = 20$

Factor the perfect square trinomial as a binomial square.

$(a - 5)^{2} = 20$

Use the square root property.

$a - 5 = \pm \sqrt{20} a - 5 = \pm \sqrt{2 \times 2 \times 5} a - 5 = \pm 2 \sqrt{5}$

Solve for a.

$a = 5 \pm 2 \sqrt{5}$

Rewrite to show two solutions.

$a = 5 + 2 \sqrt{5}, a = 5 - 2 \sqrt{5}$

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Solve the equation by completing square method.
$a^{2} - 10 a = - 5$

Short Answer

Step by step solution

Given Information

Isolate the variable terms on one side and the constant terms on the other.

Find 12b2

Factor the perfect square trinomial as a binomial square.

Solve for a.

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Solve the equation by completing square method. a2-10a=-5

Short Answer

Step by step solution

Given Information

Isolate the variable terms on one side and the constant terms on the other.

Find 12b2

Factor the perfect square trinomial as a binomial square.

Solve for a.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Geometry

Decision Maths

Discrete Mathematics

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve the equation by completing square method.
$a^{2} - 10 a = - 5$