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Q. 30

Expert-verifiedFound in: Page 29

Book edition
6th

Author(s)
Sullivan

Pages
1200 pages

ISBN
9780321795465

In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.

$5{x}^{2}=13x+6$

The required solution is $x=-\frac{2}{5},3$ and the graph of the solution is shown below:

We have:

$5{x}^{2}=13x+6$

The equation is $5{x}^{2}=13x+6$.

$5{x}^{2}-13x-6=0$

For a quadratic equation of the form $a{x}^{2}+bx+c=0$ the solutions are:

${x}_{1,\hspace{0.17em}2}=\frac{-b\pm \sqrt{{b}^{2}-4ac}}{2a}$

For $a=5,\hspace{0.17em}b=-13,\hspace{0.17em}c=-6$

${x}_{1,\hspace{0.17em}2}=\frac{-\left(-13\right)\pm \sqrt{{\left(-13\right)}^{2}-4\xb7\hspace{0.17em}5\left(-6\right)}}{2\xb7\hspace{0.17em}5}\phantom{\rule{0ex}{0ex}}{x}_{1,\hspace{0.17em}2}=\frac{-\left(-13\right)\pm \hspace{0.17em}17}{2\xb7\hspace{0.17em}5}\phantom{\rule{0ex}{0ex}}x=3,-\frac{2}{5}$

The solution of the equation is $x=-\frac{2}{5},3$.

Draw the graph of the equation $5{x}^{2}=13x+6$ using the graphing utility:

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