Question

Solve the equation$x^2+10x=-25$

$\overline{)a}$by using the Square root property

$\overline{)b}$by Completing the square

$\overline{)c}$ Which method do you prefer? Why?

Short answer

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

Step-by-step solution

Part (a) Step 1. Given information 

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

Part (a) Step 2. Calculation  

We have,

$x^2+10x=-25$

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

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

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

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

$x+5-5=0-5$

$x=-5$

Part (b) Step 1. Given information 

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

Part (b) Step 2. Calculation  

We have,

$x^2+10x=-25$

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

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

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

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

$x+5-5=0-5$

$x=-5$

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.