Chapter 10: Q 257 (page 1236)

Solve the equation by completing square method. $a^{2} = 3 a + 8$

Short Answer

Expert verified

The solutions are $a = \frac{- \sqrt{41} + 3}{2}, \frac{\sqrt{41} + 3}{2}$

Step by step solution

Given Information.

The Given equation is $a^{2} = 3 a + 8$

Isolate the variable terms on one side and the constant terms on the other.The variable terms are on the left side.

$a^{2} - 3 a = 8$

The coefficient of $a$ is $- 3$

So , $b = - 3$

Find 12b2and add to the both sides of equation.

$= {(\frac{1}{2} (- 3))}^{2} = {(\frac{- 3}{2})}^{2} = \frac{9}{4}$

Add $\frac{9}{4}$ on both side of equation

$a^{2} - 3 a + \frac{9}{4} = 8 + \frac{9}{4} a^{2} - 3 a + \frac{9}{4} = \frac{41}{4}$

Factor the perfect square trinomial as a binomial square

${(a - \frac{3}{2})}^{2} = \frac{41}{4}$

Use square root property

$(a - \frac{3}{2}) = \pm \sqrt{\frac{41}{4}} a = \pm \frac{\sqrt{41}}{2} + \frac{3}{2} a = \frac{- \sqrt{41} + 3}{2}, \frac{\sqrt{41} + 3}{2}$

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Solve the equation by completing square method. $a^{2} = 3 a + 8$

Short Answer

Step by step solution

Given Information.

Isolate the variable terms on one side and the constant terms on the other.The variable terms are on the left side.

Find 12b2and add to the both sides of equation.

Factor the perfect square trinomial as a binomial square

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Solve the equation by completing square method.a2=3a+8

Short Answer

Step by step solution

Given Information.

Isolate the variable terms on one side and the constant terms on the other.The variable terms are on the left side.

Find 12b2and add to the both sides of equation.

Factor the perfect square trinomial as a binomial square

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Discrete Mathematics

Geometry

Logic and Functions

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve the equation by completing square method. $a^{2} = 3 a + 8$