Question

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

$x^2+8=-6x$

Short answer

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

Step-by-step solution

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 x2+8=−6x in the form fx=ax2+bx+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 fx=x2+6x+8.

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

Step 4. Solve the equation x2+8=−6x from the graph of the function  fx=x2+6x+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 $x=-2$.