Question

Solve the equation by completing square method. $5q^2+70q+20=0$

Short answer

The required result is$q=-3\sqrt{5}-7,3\sqrt{5}-7$

Step-by-step solution

Given Information.    

The Given equation is $5q^2+70q+20=0$

Step 2:To complete the square, we need the coefficient of q2 to be one.Divide both side by 5 

_{$q^2+\frac{70}{5}q+4=0$}

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

$q^2+14q=-4$

The coefficient of $q$is localid="1650203073805" $14$

So ,$b=14$

Find 12b2and add to the both sides of equation.

$$\begin{gathered} ={\left(\frac{1}{2}\left(-14\right)\right)}^2 \\ ={\left(-7\right)}^2 \\ =49 \end{gathered}$$

Add $49$both side of equation

$$\begin{gathered} q^2+14q+49=-4+49 \\ {q}^2+14q+49=45 \end{gathered}$$

Factor the perfect square trinomial as a binomial square    

${\left(q+7\right)}^2=45$

Use Square root property.

$$\begin{gathered} \left(q+7\right)=\pm \sqrt{45} \\ \left(q+7\right)=\pm 3\sqrt{5} \\ q=\pm 3\sqrt{5}-7 \\ q=-3\sqrt{5}-7,3\sqrt{5}-7 \end{gathered}$$.