Question

Solve the equation by factorization: $t^2+3t-10=0$.

Answer 1

Step 1: Factorize the given equation.

Given equation: $t^2+3t-10=0$.

$$\begin{gathered} t^2+3t-10=0 \\ \Rightarrow t^2+5t-2t-10=0 \\ \Rightarrow t\left(t+5\right)-2\left(t+5\right)=0 \\ \Rightarrow \left(t+5\right)\left(t-2\right)=0 \end{gathered}$$

Step 2: Determine the roots of the equation.

Thus, the given equation can be written as, $\left(t+5\right)\left(t-2\right)=0$

So, either,

$$\begin{gathered} \left(t+5\right)=0 \\ \Rightarrow t=-5 \end{gathered}$$

Or,

$$\begin{gathered} \left(t-2\right)=0 \\ \Rightarrow t=2 \end{gathered}$$

Therefore, the solutions to the given quadratic equation are $\mathit{t}\mathbf{=}\mathbf{-}\mathbf{5}$ and $\mathit{t}\mathbf{=}\mathbf{2}$.