Chapter 7

1. $\begin{array}{l} 2 x^{2} + 5 x = 12 \\ 2 x^{2} + 5 x - 12 = 0 \\ (2 x - 3) (x + 4) = 0 \\ \begin{array}{l} 2 x - 3 = 0 & x + 4 = 0 \end{array} \\ \begin{array}{l} x = \frac{3}{2} & or & x = - 4 \end{array} \end{array}$
2. $\begin{array}{l} x^{2} = 3 x + 5 \\ x^{2} - 3 x - 5 = 0 \\ \begin{array}{l} a = 1, & b = - 3, & c = - 5 \end{array} \\ \begin{array}{rcl} x & = & \frac{- (- 3) \pm \sqrt{{(- 3)}^{2} - 4 (1) (- 5)}}{2 (1)} \\ = & \frac{3 \pm \sqrt{29}}{2} \end{array} \end{array}$
3. $4 x^{2} - 5 x - 3 = 0$

On calculator

$Y_{1} = 4 X^{2} - 5 X - 3$

From zero feature

$\begin{array}{l} x = - 0.44 & or & x = 1.69 \end{array}$
4. $\begin{array}{rcl} 2 x^{2} - x & = & 6 - 2 x (3 - x) \\ 2 x^{2} - x & = & 6 - 6 x + 2 x^{2} \\ 5 x & = & 6 (not quadratic) \\ x & = & \frac{6}{5} \end{array}$
5. $\begin{array}{rcl} \frac{3}{x} - \frac{2}{x + 2} = 1 LCD & = & x (x + 2) \\ \frac{3 x (x + 2)}{x} - \frac{2 x (x + 2)}{x + 2} & = & x (x + 2) \\ 3 (x + 2) - 2 x & = & x^{2} + 2 x \\ 3 x + 6 - 2 x & = & x^{2} + 2 x \\ 0 & = & x^{2} + x - 6 \\ (x + 3) (x - 2) & = & 0 \\ x & = & - 3, 2 \end{array}$
6. $\begin{array}{l} y = 2 x^{2} + 8 x + 5 \\ \frac{- b}{2 a} = \frac{- 8}{2 (2)} = - 2 \\ y = 2 {(- 2)}^{2} + 8 (- 2) + 5 = - 3 \end{array}$

Min. pt. $(a > 0)$ is $(- 2, - 3),$

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Basic Technical Mathematics, 11th Edition by Allyn J. Washington, Richard Evans