# Chapter 9 - Quadratic Functions and Equations - 9-6 The Quadratic Formula and the Discriminant - Practice and Problem-Solving Exercises - Page 571: 7

x=$\frac{-3}{2}$, -1

#### Work Step by Step

The quadratic formula states that if a$x^{2}$+bx+c=0, and a$\ne$0, then $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$. If 2$x^{2}$+5x+3=0, then a=2, b=5, and c=3, and to solve for x, then all we must do is plug the numbers into the quadratic formula then simplify. $x=\frac{-5\pm\sqrt{(5)^2-4(2)(3)}}{2(2)}$ =$\frac{-5\pm\sqrt{25-24}}{4}$ (5 squared=25, 4*2*3=24, and 2*2=4) =$\frac{-5\pm\sqrt{1}}{4}$ (25-24=1) =$\frac{-5\pm1}{4}$ ($\sqrt 1$=1) Since there is a plus minus symbol, we of course need to make sure that we compute both of our answers. x=$\frac{-5+1}{4}$=$\frac{-4}{4}$=-1 x=$\frac{-5-1}{4}$=$\frac{-6}{4}$=$\frac{-3}{2}$

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