Q10. - Algebra 1

Question

Solve each equation by graphing. If integral roots cannot be found, estimate the roots to the nearest tenth.

 $x^2+8=-6x$

Step-by-Step Solution

Answer

The roots of the equation $x^2+8=-6x$ are $x=-4$ and $x=-2$.

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

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

Step 2. Rewrite the equation x 2 + 8 = − 6 x in the form f x = a x 2 + b x + c .

Write the equation $x^2+8=-6x$ in standard form.

The standard form is

 $x^2+6x+8=0$

Write the equation $x^2+6x+8=0$ in the form $f\left(x\right)=a{x}^2+bx+c$.

$f\left(x\right)=x^2+6x+8$

 

Step 3. Plot the graph of the function f x = x 2 + 6 x + 8 .

The graph of the function $f\left(x\right)=x^2+6x+8$ is shown below.

Step 4. Solve the equation x 2 + 8 = − 6 x from the graph of the function f x = x 2 + 6 x + 8 .

Observe the graph of the function $f\left(x\right)=x^2+6x+8$.

The graph intersects the  - axis at the points $x=-4$ and $x=-2$.  

Therefore the roots of the equation $x^2+8=-6x$ are $x=-4$ and $x=-2$.