Chapter 9.6, Problem 54SR

To determine

The equation $x^2+6x+9=16$ by taking square root

Answer to Problem 54SR

The solution of the equation is $x=1$ .

Explanation of Solution

Given:

The equation $x^2+6x+9=16$ .

Concept Used:

• To get rid of a number in addition from one side, subtract the same number from both sides of equal sign.
• To get rid of a number in subtraction from one side, add the same number both sides of equal sign.
• To get rid of a number in multiplication from one side, divide the same number from both sides of equal sign.
• To get rid of a number in division from one side, multiply the same number both sides of equal sign.

Rules of Addition/ Subtraction:

• Two numbers with similar sign always get added and the resulting number will carry the similar sign.
• Two numbers with opposite signs always get subtracted and the resulting number will carry the sign of larger number.

Rules of Multiplication/ Division:

• The product/quotient of two similar sign numbers is always positive.
• The product/quotient of two numbers with opposite signs is always negative.

Calculation:

In order to solve the given equation $x^2+6x+9=16$ for the variable, isolate the variable term x on one side by performing some basic algebraic operations to get rid of the other numbers and terms associated with it.

Here to isolate x on left side, take the square root both sides as shown below,

  $\begin{array}{l}{x}^2+6x+9=16\\ x^2+2\times 3x+{\left(3\right)}^2=4\times 4\\ {\left(x+3\right)}^2=4^2\\ \text{Taking}\text{square}\text{root}\\ \sqrt{{\left(x+3\right)}^2}=\sqrt{4^2}\\ x+3=4\\ x+3-3=4-3\\ x=1\end{array}$

Thus, the solution of the equation is $x=1$ .