Q23. - Algebra 1

Question

Solve the equation by completing the square. Round to the nearest tenth.

$x^2-10x=-24$

Step-by-Step Solution

Answer

$\mathit{x}\mathbf{=}\mathbf{4}\mathbf{,}\mathbf{6}$ are the solutions of the given equation.

Step 1. Define the standard form of the quadratic equation.

A quadratic equation, which is written in the form, $a{x}^2+bx+c=0$, where, $a\ne 0$ is called the standard form of the quadratic equation.

Step 2. Define the quadratic formula.

For the quadratic equation $a{x}^2+bx+c=0,$ where, $a\ne 0$ is given by 

 $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Step 3. Solve the equation x 2 − 10 x = − 24 by completing the square.

Change the equation $x^2-10x=-24$ in standard form.

The standard form is

$x^2-10x+24=0$

Compare the quadratic equation $x^2-10x+24=0$ with the quadratic equation $a{x}^2+bx+c=0$.

$a=1,b=-10,c=24$

Substitute, $a=1,b=-10$ and $c=24$ in $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$.

$$\begin{gathered} x=\frac{-\left(-10\right)\pm \sqrt{{\left(-10\right)}^2-4\left(1\right)\left(24\right)}}{2\left(1\right)} \\ x=\frac{10\pm \sqrt{100-96}}{2} \\ x=\frac{10\pm \sqrt{4}}{2} \\ x=\frac{10\pm 2}{2} \\ x=\frac{10-2}{2},\frac{10+2}{2} \\ x=\frac{8}{2},\frac{12}{2} \\ x=4,6 \end{gathered}$$

Hence, $x=4,6$ are the solutions of the given equation.