Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 10 - Quadratic Equations - 10.3 - Quadratic Formula - Problem Set 10.3 - Page 453: 15



Work Step by Step

Step 1: $2x^{2}=7x$ can also be written as $2x^{2}-7x+0=0$. Comparing $2x^{2}-7x+0=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we obtain: $a=2$, $b=-7$, and $c=0$ Step 2: The quadratic formula is: $x=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$ Step 3: Substituting the values of a,b, and c in the formula, we obtain: $x=\frac{-(-7) \pm \sqrt {(-7)^{2}-4(2)(0)}}{2(2)}$ Step 4: $x=\frac{7 \pm \sqrt {49-0}}{4}$ Step 5: $x=\frac{7 \pm \sqrt {49}}{4}$ Step 6: $x=\frac{7 \pm 7}{4}$ Step 7: $x=\frac{7+7}{4}$ or $x=\frac{7-7}{4}$ Step 8: $x=\frac{14}{4}$ or $x=\frac{0}{4}$ Step 9: $x=\frac{7}{2}$ or $x=0$ Step 10: Therefore, the solution set is {$0,\frac{7}{2}$}.
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