Question

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

$6x^2-13x=15$

Short answer

The roots of the equation$6x^2-13x=15$ are$\mathit{x}\mathbf{=}\mathbf{-}\mathbf{0}\mathbf{.8}$ and $\mathit{x}\mathbf{=}\mathbf{3}$.

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 + in the form +. 

Write the equation $6x^2-13x=15$ in standard form.

This standard form is

$6x^2-13x-15=0$

Write the equation $6x^2-13x-15=0$ in the form $f\left(x\right)=a{x}^2+bx+c$.

$f\left(x\right)=6x^2-13x-15$

Step 3. Plot the graph of the function fx=6x2−13x−15.

The graph of the function $f\left(x\right)=6x^2-13x-15$is shown below.

Step 4. Solve the equation 6x2−13x=15 from the graph of the function fx=6x2−13x−15. 

Observe the graph of the function $f\left(x\right)=6x^2-13x-15$.

The graph intersects the $x$-axis at the points near about $x=-0.8$and $x=3$.

Therefore the roots of the equation $x^2-10x=-21$ are $x=-0.8$ and $x=3$.