Question

Solve quadratic equations of the form $x^2+bx+c=0$by completing the square.

In the following exercises, solve by completing the square.

$t^2-10t-6=5$

Short answer

The required value of$t$ is$11,-1$

Step-by-step solution

Given information

$t^2-10t-6=5$

Calculation

$$\begin{gathered} t^2-10t-6=5 \\ \Rightarrow t^2-10t=5+6 \\ \Rightarrow t^2-10t=11 \\ \Rightarrow t^2-10t+(\frac{1}{2}\times {(-10))}^2=11+25 \\ \Rightarrow t^2-10t+25=11+25 \\ \Rightarrow {(t-5)}^2=36\Rightarrow t-5=\pm \sqrt{36}=\pm 6 \\ \Rightarrow t=5\pm 6 \\ =5+6,5-6 \\ =11,-1 \end{gathered}$$

The required value of$t$is$11,-1$