Question

Solve the quadratic equation $(x+3)(x-2)=2(x+11)$ by using the quadratic formula.

Answer 1

Step 1: Writing the given quadratic equation in the standard form

The standard form of the quadratic equation is $a{x}^2+bx+c=0$.

$$\begin{gathered} (x+3)(x-2)=2(x+11) \\ \Rightarrow x(x-2)+3(x-2)=2x+22 \\ \Rightarrow x^2-2x+3x-6=2x+22 \\ \Rightarrow x^2-x-28=0 \end{gathered}$$

Step 2: Determining the value of $x$ by using the quadratic formula

The quadratic formula is $\begin{array}{rcl}x& =& \frac{-b\pm \sqrt{b^2-4ac}}{2a}\end{array}$.

For the equation $x^2-x-28=0$, the value of variables are $a=1,b=-1$ and $c=-28$.

Substituting the values of $a,b$ and $c$ in quadratic formula,

$$\begin{gathered} x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ \Rightarrow x=\frac{-(-1)\pm \sqrt{{(-1)}^2-4\left(1\right)(-28)}}{2\left(1\right)} \\ \Rightarrow x=\frac{1\pm \sqrt{1+112}}{2} \\ \Rightarrow x=\frac{1\pm \sqrt{113}}{2} \\ \therefore x=\frac{1-\sqrt{113}}{2},\frac{1+\sqrt{113}}{2} \end{gathered}$$

Therefore, the value of $x$ is either $\frac{1-\sqrt{113}}{2}$ or $\frac{1+\sqrt{113}}{2}$.