Q19. - Algebra 1

Question

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

$x^2+4x+2=0$

Step-by-Step Solution

Answer

 $\mathit{x}\mathbf{=}\mathbf{0}\mathbf{.6}\mathbf{,}\mathbf{3}\mathbf{.4}$ 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 perfect square a + b 2 .

${\left(a+b\right)}^2=a^2+2ab+b^2\mathrm{...........}\left(1\right)$

Step 3. Solve the equation x 2 + 4 x + 2 = 0 by completing the square.

Use (1) to solve the equation.

$$\begin{gathered} x^2+4x+2=0 \\ x^2+2\left(x\right)\left(2\right)+2=0 \\ {x}^2+2\left(x\right)\left(2\right)+2^2+2=2^2 \\ {\left(x+2\right)}^2+2=4 \end{gathered}$$

                    $$\begin{gathered} {\left(x+2\right)}^2=4-2 \\ {\left(x+2\right)}^2=2 \\ x+2=\pm \sqrt{2} \\ x=2\pm \sqrt{2} \\ x=2-\sqrt{2},2+\sqrt{2} \end{gathered}$$

Use calculator.

$\begin{array}{l}x=0.585786437,3.414213562\\ x\simeq 0.6,3.4\end{array}$

Hence, $x=0.6,3.4$ are the solutions of the given equation.