Chapter 9: Q. 111 E (page 886)

Solve the equation $x^{2} + 10 x = - 25$
$a$ by using the Square root property
$b$ by Completing the square
$c$ Which method do you prefer? Why?

Short Answer

Expert verified

The solution is $x = - 5$ . The preferred method is Completing the square .

Step by step solution

Part (a) Step 1. Given information

Equation: $x^{2} + 10 x = - 25$

Part (a) Step 2. Calculation

We have,

$x^{2} + 10 x = - 25$

$x^{2} + 10 x + {(\frac{1}{2} \cdot (10))}^{2} = - 25 + {(\frac{1}{2} \cdot (10))}^{2}$

$x^{2} + 10 x + 25 = - 25 + 25$

${(x + 5)}^{2} = 0$

localid="1645186040786" $\sqrt{{(x + 5)}^{2}} = \sqrt{0}$ using the Square root property

$x + 5 - 5 = 0 - 5$

$x = - 5$

Part (b) Step 1. Given information

Equation: $x^{2} + 10 x = - 25$

Part (b) Step 2. Calculation

We have,

$x^{2} + 10 x = - 25$

localid="1645185232165" $x^{2} + 10 x + {(\frac{1}{2} \cdot (10))}^{2} = - 25 + {(\frac{1}{2} \cdot (10))}^{2}$ using Completing the square

$x^{2} + 10 x + 25 = - 25 + 25$

localid="1645186141392" ${(x + 5)}^{2} = 0$

$\sqrt{{(x + 5)}^{2}} = \sqrt{0}$

$x + 5 - 5 = 0 - 5$

$x = - 5$

Part (c) Step 1. Explanation

I prefer Completing the square method since all quadratic equations can be solved by Completing the square. Whereas, Square root property is used to solve equations only when the left side is a perfect square.

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Solve the equation $x^{2} + 10 x = - 25$
$a$ by using the Square root property
$b$ by Completing the square
$c$ Which method do you prefer? Why?

Short Answer

Step by step solution

Part (a) Step 1. Given information

Part (a) Step 2. Calculation

Part (b) Step 1. Given information

Part (b) Step 2. Calculation

Part (c) Step 1. Explanation

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Solve the equationx2+10x=-25aby using the Square root propertybby Completing the squarec Which method do you prefer? Why?

Short Answer

Step by step solution

Part (a) Step 1. Given information

Part (a) Step 2. Calculation

Part (b) Step 1. Given information

Part (b) Step 2. Calculation

Part (c) Step 1. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Decision Maths

Applied Mathematics

Statistics

Logic and Functions

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Solve the equation $x^{2} + 10 x = - 25$
$a$ by using the Square root property
$b$ by Completing the square
$c$ Which method do you prefer? Why?