Question

Solve the equation by completing square method.

$t^2-14t=-50$

Short answer

The equation has no real solutions.

Step-by-step solution

Given Information  

The Given equation is $t^2-14t=-50$.

Isolate the variable terms on one side and the constant terms on the other. 

The variable terms are on the left side.

$t^2-14t=-50$

Here,$b=-14$

Find 12b2 and add to the both sides of equation.  

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

Add $49$both sides.

$$\begin{gathered} t^2-14t+49=-50+49 \\ {t}^2-14t+49=-1 \end{gathered}$$

Factor the perfect square trinomial as a binomial square.  

$(t-7{)}^2=-1$

Use the square root property.

$t-7=\pm \sqrt{-1}$

Since $\sqrt{-1}$is not a real number.

Thus, the equation has no real solutions.