Big Ideas Math - Algebra 1, A Common Core Curriculum

Published by Big Ideas Learning LLC
ISBN 10: 978-1-60840-838-2
ISBN 13: 978-1-60840-838-2

Chapter 9 - Solving Quadratic Equations - 9.5 - Solving Quadratic Equations Using the Quadratic Formula - Exercises - Page 521: 38

Answer

The solutions are $x=8$ and $x=-5$.

Work Step by Step

The given equation is $\Rightarrow x^2-3x-40=0$ The equation is easily factorable. So, solve by factoring. $\Rightarrow x^2-3x-40=0$ Rewrite $-3x$ as $-8x+5x$. $\Rightarrow x^2-8x+5x-40=0$ Group the terms. $\Rightarrow (x^2-8x)+(5x-40)=0$ Factor each group. $\Rightarrow x(x-8)+5(x-8)=0$ Factor out $(x-8)$. $\Rightarrow (x-8)(x+5)=0$ Use zero-product property. $\Rightarrow x-8=0$ or $x+5=0$ Solve for $x$. $\Rightarrow x=8$ or $x=-5$ Hence, the solutions are $x=8$ and $x=-5$.
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