9.4 Solve Equations in Quadratic Form

Before you get started, take this readiness quiz.

Factor by substitution: $y^{4} - y^{2} - 20 .$
If you missed this problem, review the reference.

Factor by substitution: $\left(y - 4\right)^{2} + 8 \left(y - 4\right) + 15 .$
If you missed this problem, review the reference.

Simplify: ⓐ $x^{\frac{1}{2}} \cdot x^{\frac{1}{4}}$ ⓑ $\left(x^{\frac{1}{3}}\right)^{2}$ ⓒ $\left(x^{−1}\right)^{2} .$
If you missed this problem, review the reference.

Solve: $x^{4} - 6 x^{2} + 8 = 0$.

Solve: $x^{4} - 11 x^{2} + 28 = 0$.

Solve: $\left(x - 5\right)^{2} + 6 \left(x - 5\right) + 8 = 0 .$

Solve: $\left(y - 4\right)^{2} + 8 \left(y - 4\right) + 15 = 0 .$

Solve: $x - 7 \sqrt{x} + 12 = 0 .$

Solve: $x - 6 \sqrt{x} + 8 = 0 .$

Solve: $x^{\frac{2}{3}} - 5 x^{\frac{1}{3}} - 14 = 0 .$

Solve: $x^{\frac{1}{2}} - 8 x^{\frac{1}{4}} + 15 = 0 .$

Solve: $8 x^{−2} - 10 x^{−1} + 3 = 0 .$

Solve: $6 x^{−2} - 23 x^{−1} + 20 = 0 .$

Solve.

$x^{4} - 7 x^{2} + 12 = 0$

Solve.

$x^{4} - 13 x^{2} - 30 = 0$

Solve.

$2 x^{4} - 5 x^{2} + 3 = 0$

Solve.

$2 x^{4} - 7 x^{2} + 3 = 0$

Solve.

$\left(x - 3\right)^{2} - 5 \left(x - 3\right) - 36 = 0$

Solve.

$\left(3 y + 2\right)^{2} + \left(3 y + 2\right) - 6 = 0$

Solve.

$\left(x^{2} + 1\right)^{2} - 5 \left(x^{2} + 1\right) + 4 = 0$

Solve.

$2 \left(x^{2} - 5\right)^{2} - 5 \left(x^{2} - 5\right) + 2 = 0$

Solve.

$x - \sqrt{x} - 20 = 0$

Solve.

$x + 6 \sqrt{x} - 16 = 0$

Solve.

$6 x + \sqrt{x} - 2 = 0$

Solve.

$10 x - 17 \sqrt{x} + 3 = 0$

Solve.

$x^{\frac{2}{3}} + 9 x^{\frac{1}{3}} + 8 = 0$

Solve.

$x^{\frac{2}{3}} + 4 x^{\frac{1}{3}} = 12$

Solve.

$6 x^{\frac{2}{3}} - x^{\frac{1}{3}} = 12$

Solve.

$8 x^{\frac{2}{3}} - 43 x^{\frac{1}{3}} + 15 = 0$

Solve.

$x - 8 x^{\frac{1}{2}} + 7 = 0$

Solve.

$6 x^{−2} + 13 x^{−1} + 5 = 0$

Solve.

$8 x^{−2} - 2 x^{−1} - 3 = 0$

Explain how to recognize an equation in quadratic form.