Question

How do you solve this equation using the square root property ${{\left( x+3 \right)}^{2}}=49$?

Answer 1

Hint: In this problem we need to solve the given equation by using the square root property. We know that the solution of the equation is the value of the variable for which the given equation is satisfied. For this we will apply the reverse operations for the operations which are in the given equation. We can observe the square function in the given equation, so we will first apply the square root function on both sides of the given equation. Now we will simplify the obtained equation by applying the algebraic formulas and know values. Now we will apply the subtraction operation which is the reverse operation for the addition. Now we will simplify the obtained equations to get the required solution.

Complete step by step solution:
Given that, ${{\left( x+3 \right)}^{2}}=49$.
Applying square root on both sides of the above equation to solve the equation, then we will get
$\Rightarrow \sqrt{{{\left( x+3 \right)}^{2}}}=\sqrt{49}$
We know that the square root and square functions are cancelled and the value of $\sqrt{49}={{\left( \pm 7 \right)}^{2}}$. Substituting these values in the above equation, then we will get
$\Rightarrow x+3=\pm 7$
Separating the above equation as two equation which are
$x+3=7$ or $x+3=-7$
Subtracting the $3$ from the both of the above equation, then we will get
$\begin{align}
  & \Rightarrow x+3-3=7-3 \\
 & \Rightarrow x=4 \\
\end{align}$ or $\begin{align}
  & \Rightarrow x+3-3=-7-3 \\
 & \Rightarrow x=-10 \\
\end{align}$

Hence the solution of the given equation ${{\left( x+3 \right)}^{2}}=49$ is $x=4,-10$.

Note: In this problem they have asked to solve the given equation by using square root method, so we have followed the above procedure. We can also solve the equation in another method. In this method we will expand the term ${{\left( x+3 \right)}^{2}}$ by using the algebraic formula ${{\left( a+b \right)}^{2}}={{a}^{2}}+{{b}^{2}}+2ab$ and simplify the obtained equation and convert it in the form of standard quadratic equation. From this we can use either factorization method or we can use the formula $x=\dfrac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a}$ to get the solution.