Q21. - Algebra 1

Question

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

$6x^2-13x=15$

Step-by-Step Solution

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 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 f x = 6 x 2 − 13 x − 15 .

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

Step 4. Solve the equation 6 x 2 − 13 x = 15 from the graph of the function f x = 6 x 2 − 13 x − 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 $x=3$.