Chapter 6

Solve each equation. $$\frac{16}{x+5}-\frac{12}{x}=-2$$

Use the quadratic formula to solve each of the quadratic equations. Check your solutions by using the sum and product relationships. $$3 x^{2}-2 x+5=0$$

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

Solve each radical equation. Don't forget, you must check potential solutions. $$\sqrt{5 x}+10=x$$

Add or subtract as indicated. $$\left(\frac{3}{8}-\frac{5}{2} i\right)-\left(\frac{5}{6}+\frac{1}{7} i\right)$$

Solve each inequality. $$8 x^{2}+22 x+5 \geq 0$$

Solve each equation. $$\frac{3}{x-1}-\frac{2}{x}=\frac{5}{2}$$

Use the quadratic formula to solve each of the quadratic equations. Check your solutions by using the sum and product relationships. $$3 a^{2}-8 a+2=0$$

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

Solve each equation for \(x\) by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). $$x^{2}-5 k x=0$$

Write each of the following in terms of \(i\) and simplify. For example, $$ \sqrt{-20}=i \sqrt{20}=i \sqrt{4} \sqrt{5}=2 i \sqrt{5} $$ $$\sqrt{-81}$$

Solve each inequality. $$12 x^{2}-20 x+3 \geq 0$$

Solve each equation. $$\frac{4}{x+1}+\frac{2}{x}=\frac{5}{3}$$

Use the quadratic formula to solve each of the quadratic equations. Check your solutions by using the sum and product relationships. $$2 a^{2}-6 a+1=0$$

Use the method of completing the square to solve each quadratic equation. $$x^{2}+5 x-3=0$$

Solve each equation for \(x\) by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). $$x^{2}+7 k x=0$$

Write each of the following in terms of \(i\) and simplify. For example, $$ \sqrt{-20}=i \sqrt{20}=i \sqrt{4} \sqrt{5}=2 i \sqrt{5} $$ $$\sqrt{-49}$$

Solve each inequality. $$x(5 x-36)>32$$

Solve each equation. $$\frac{6}{x}+\frac{40}{x+5}=7$$

Use the quadratic formula to solve each of the quadratic equations. Check your solutions by using the sum and product relationships. $$-2 n^{2}+3 n+5=0$$

Use the method of completing the square to solve each quadratic equation. $$x^{2}+5 x+1=0$$

Solve each equation for \(x\) by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). $$x^{2}=16 k^{2} x$$

Write each of the following in terms of \(i\) and simplify. For example, $$ \sqrt{-20}=i \sqrt{20}=i \sqrt{4} \sqrt{5}=2 i \sqrt{5} $$ $$\sqrt{-14}$$

Solve each inequality. $$x(7 x+40)<12$$

Solve each equation. $$\frac{12}{t}+\frac{18}{t+8}=\frac{9}{2}$$

Use the quadratic formula to solve each of the quadratic equations. Check your solutions by using the sum and product relationships. $$-3 n^{2}-11 n+4=0$$

Use the method of completing the square to solve each quadratic equation. $$x^{2}+7 x+2=0$$

Solve each equation for \(x\) by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). $$x^{2}=25 k^{2} x$$

Write each of the following in terms of \(i\) and simplify. For example, $$ \sqrt{-20}=i \sqrt{20}=i \sqrt{4} \sqrt{5}=2 i \sqrt{5} $$ $$\sqrt{-33}$$

Solve each inequality. $$x^{2}-14 x+49 \geq 0$$

Solve each equation. $$\frac{5}{n-3}-\frac{3}{n+3}=1$$

Use the quadratic formula to solve each of the quadratic equations. Check your solutions by using the sum and product relationships. $$3 x^{2}+19 x+20=0$$

Use the method of completing the square to solve each quadratic equation. $$y^{2}-7 y+3=0$$

Solve each equation for \(x\) by factoring and applying the property, \(a b=0\) if and only if \(a=0\) or \(b=0\). $$x^{2}-12 k x+35 k^{2}=0$$

Write each of the following in terms of \(i\) and simplify. For example, $$ \sqrt{-20}=i \sqrt{20}=i \sqrt{4} \sqrt{5}=2 i \sqrt{5} $$ $$\sqrt{-\frac{16}{25}}$$

Solve each inequality. $$(x+9)^{2} \geq 0$$

Solve each equation. $$\frac{3}{t+2}+\frac{4}{t-2}=2$$

Use the quadratic formula to solve each of the quadratic equations. Check your solutions by using the sum and product relationships. $$2 x^{2}-17 x+30=0$$

Use the method of completing the square to solve each quadratic equation. $$y^{2}-9 y+30=0$$

Write each of the following in terms of \(i\) and simplify. For example, $$ \sqrt{-20}=i \sqrt{20}=i \sqrt{4} \sqrt{5}=2 i \sqrt{5} $$ $$\sqrt{-\frac{64}{36}}$$

Solve each inequality. $$4 x^{2}+20 x+25 \leq 0$$

Solve each equation. $$x^{4}-18 x^{2}+72=0$$

Use the quadratic formula to solve each of the quadratic equations. Check your solutions by using the sum and product relationships. $$36 n^{2}-60 n+25=0$$

Use the method of completing the square to solve each quadratic equation. $$2 x^{2}+4 x-3=0$$

Write each of the following in terms of \(i\) and simplify. For example, $$ \sqrt{-20}=i \sqrt{20}=i \sqrt{4} \sqrt{5}=2 i \sqrt{5} $$ $$\sqrt{-18}$$

Solve each inequality. $$9 x^{2}-6 x+1 \leq 0$$

Solve each equation. $$x^{4}-21 x^{2}+54=0$$

Use the quadratic formula to solve each of the quadratic equations. Check your solutions by using the sum and product relationships. $$9 n^{2}+42 n+49=0$$

Use the method of completing the square to solve each quadratic equation. $$2 t^{2}-4 t+1=0$$

Write each of the following in terms of \(i\) and simplify. For example, $$ \sqrt{-20}=i \sqrt{20}=i \sqrt{4} \sqrt{5}=2 i \sqrt{5} $$ $$\sqrt{-84}$$