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: 34

Answer

{$\frac{5}{3}$}

Work Step by Step

Step 1: Comparing $9x^{2}-30x+25=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we find: $a=9$, $b=-30$ and $c=25$ 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: $x=\frac{-(-30) \pm \sqrt {(-30)^{2}-4(9)(25)}}{2(9)}$ Step 4: $x=\frac{30 \pm \sqrt {900-900}}{18}$ Step 5: $x=\frac{30 \pm \sqrt {0}}{18}$ Step 6: $x=\frac{30 \pm 0}{18}$ Step 7: $x=\frac{30}{18}$ Step 8: $x=\frac{5}{3}$ Step 9: Therefore, the solution set is {$\frac{5}{3}$}.
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