Question

Solve the quadratic equation by completing the square.4a²- 48a +52 = 0a= _,_

Answer 1

Given

`4a^2-48a+52=0`

Solution

`\begin{gathered} 4a^2-48a+52=0 \\ So\text{ divide both sides by 4} \\ (4a^2)/(4)-(48a)/(4)+(52)/(4)=0 \\ which\text{ gives } \\ a^2-12a+13=0 \\ Keep\text{ a on LHS} \\ a^2-12a=-13 \\ Take\text{ the half of coefficient of a and square it} \\ (-(12)/(2))^2=36 \\ \\ rewrite\text{ as perfect square} \\ \\ (a-6)^2=-13+36 \\ (a-6)^2=23 \\ \end{gathered}`

`\begin{gathered} a-6=\pm√(23) \\ a=6\pm√(23) \end{gathered}`

`\begin{gathered} a=10.79583\text{ ,}a=1.20416 \\ or \\ a=6+√(23),\:a=6-√(23)\quad \\ \\ \end{gathered}`