Chapter 6

Simplify and reduce each expression. $$ \frac{-6 \pm \sqrt{48}}{4} $$

Solve each quadratic equation by using (a) the factoring method and (b) the method of completing the square. $$ 2 n^{2}-n-15=0 $$

Solve each of the quadratic equations by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). If necessary, return to Chapter 3 and review the factoring techniques presented there. $$ x^{2}+x-30=0 $$

Solve each inequality and graph its solution set on a number line. $$ (x+2)(x+1)(x-2)>0 $$

Solve each quadratic equation using the method that seems most appropriate to you. $$ 28-x-2 x^{2}=0 $$

Simplify and reduce each expression. $$ \frac{-8 \pm \sqrt{72}}{4} $$

Solve each quadratic equation by using (a) the factoring method and (b) the method of completing the square. $$ 3 n^{2}+n-14=0 $$

Solve each of the quadratic equations by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). If necessary, return to Chapter 3 and review the factoring techniques presented there. $$ x^{2}-8 x-48=0 $$

Add or subtract as indicated. $$ (5+2 i)+(7+10 i) $$

Solve each inequality and graph its solution set on a number line. $$ x(x+2)(x-4) \leq 0 $$

Solve each quadratic equation using the method that seems most appropriate to you. $$ (x-2)(x+9)=-10 $$

Simplify and reduce each expression. $$ x^{2}+2 x-1=0 $$

Solve each quadratic equation by using (a) the factoring method and (b) the method of completing the square. $$ 3 n^{2}+7 n-6=0 $$

Solve each of the quadratic equations by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). If necessary, return to Chapter 3 and review the factoring techniques presented there. $$ x^{2}-19 x+84=0 $$

Add or subtract as indicated. $$ (-8+4 i)+(2+6 i) $$

Solve each inequality and graph its solution set on a number line. $$ x(x+3)(x-3) \leq 0 $$

Solve each quadratic equation using the method that seems most appropriate to you. $$ (x+3)(2 x+1)=-3 $$

Simplify and reduce each expression. $$ x^{2}+4 x-1=0 $$

Solve each quadratic equation by using (a) the factoring method and (b) the method of completing the square. $$ 2 n^{2}+7 n-4=0 $$

Solve each of the quadratic equations by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). If necessary, return to Chapter 3 and review the factoring techniques presented there. $$ x^{2}-21 x+104=0 $$

Add or subtract as indicated. $$ (5-8 i)+(-7+2 i) $$

Solve each inequality. $$ x^{2}+2 x-35<0 $$

Solve each quadratic equation using the method that seems most appropriate to you. $$ 2 x^{2}-4 x+7=0 $$

Solve each quadratic equation by using (a) the factoring method and (b) the method of completing the square. $$ n(n+6)=160 $$

Solve each of the quadratic equations by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). If necessary, return to Chapter 3 and review the factoring techniques presented there. $$ 2 x^{2}+19 x+24=0 $$

Add or subtract as indicated. $$ (3+2 i)-(5+7 i) $$

Solve each inequality. $$ x^{2}+3 x-54<0 $$

Solve each quadratic equation using the method that seems most appropriate to you. $$ 3 x^{2}-2 x+8=0 $$

Simplify and reduce each expression. $$ n^{2}+3 n-2=0 $$

Solve each quadratic equation by using (a) the factoring method and (b) the method of completing the square. $$ n(n-6)=216 $$

Solve each of the quadratic equations by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). If necessary, return to Chapter 3 and review the factoring techniques presented there. $$ 4 x^{2}+29 x+30=0 $$

Add or subtract as indicated. $$ (1+3 i)-(4+9 i) $$

Solve each inequality. $$ x^{2}-11 x+28>0 $$

Solve each quadratic equation using the method that seems most appropriate to you. $$ x^{2}-18 x+15=0 $$

Simplify and reduce each expression. $$ a^{2}-8 a=4 $$

Use the method of completing the square to solve each quadratic equation. $$ x^{2}+4 x-2=0 $$

Solve each of the quadratic equations by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). If necessary, return to Chapter 3 and review the factoring techniques presented there. $$ 15 x^{2}+29 x-14=0 $$

Add or subtract as indicated. $$ (-7+3 i)-(5-2 i) $$

Solve each inequality. $$ x^{2}+11 x+18>0 $$

Solve each quadratic equation using the method that seems most appropriate to you. $$ x^{2}-16 x+14=0 $$

Simplify and reduce each expression. $$ a^{2}-6 a=2 $$

Use the method of completing the square to solve each quadratic equation. $$ x^{2}+2 x-1=0 $$

Solve each of the quadratic equations by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). If necessary, return to Chapter 3 and review the factoring techniques presented there. $$ 24 x^{2}+x-10=0 $$

Add or subtract as indicated. $$ (-8+4 i)-(9-4 i) $$

Solve each inequality. $$ 3 x^{2}+13 x-10 \leq 0 $$

Solve each quadratic equation using the method that seems most appropriate to you. $$ 20 y^{2}+17 y-10=0 $$

Use the method of completing the square to solve each quadratic equation. $$ x^{2}+6 x-3=0 $$

Solve each of the quadratic equations by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). If necessary, return to Chapter 3 and review the factoring techniques presented there. $$ 25 x^{2}-30 x+9=0 $$

Add or subtract as indicated. $$ (-3-10 i)+(2-13 i) $$

Solve each inequality. $$ 4 x^{2}-x-14 \leq 0 $$