10.1 Solve Quadratic Equations Using the Square Root Property

Before you get started, take this readiness quiz.

Simplify: $\sqrt{75}$.
If you missed this problem, review the reference.

Simplify: $\sqrt{\frac{64}{3}}$.
If you missed this problem, review the reference.

Factor: $4 x^{2} - 12 x + 9$.
If you missed this problem, review the reference.

Solve: $x^{2} = 169$.

Solve: $x^{2} = 81$.

Solve: $y^{2} = 121$.

Solve: $x^{2} - 50 = 0$.

Solve: $y^{2} - 27 = 0$.

Solve: $2 x^{2} = 98$.

Solve: $3 z^{2} = 108$.

Solve: $q^{2} + 24 = 0$.

Solve: $c^{2} + 12 = 0$.

Solve: $d^{2} + 81 = 0$.

Solve: $\frac{1}{2} x^{2} + 4 = 24$.

Solve: $\frac{3}{4} y^{2} - 3 = 18$.

Solve: $2 c^{2} - 4 = 45$.

Solve: $5 r^{2} - 2 = 34$.

Solve: $3 t^{2} + 6 = 70$.

Solve: $\left(q + 5\right)^{2} = 1$.

Solve: $\left(r - 3\right)^{2} = 25$.

Solve: $\left(a - 3\right)^{2} = 18$.

Solve: $\left(b + 2\right)^{2} = 40$.

Solve: $\left(x - \frac{1}{2}\right)^{2} = \frac{5}{4} .$

Solve: $\left(x - \frac{1}{3}\right)^{2} = \frac{5}{9} .$

Solve: $\left(y - \frac{3}{4}\right)^{2} = \frac{7}{16} .$

Solve: $\left(x - 2\right)^{2} + 3 = 30$.

Solve: $\left(a - 5\right)^{2} + 4 = 24$.

Solve: $\left(b - 3\right)^{2} - 8 = 24$.

Solve: $\left(3 v - 7\right)^{2} = −12$.

Solve: $\left(3 r + 4\right)^{2} = −8$.

Solve: $\left(2 t - 8\right)^{2} = −10$.

Solve: $p^{2} - 10 p + 25 = 18$.

Solve: $x^{2} - 6 x + 9 = 12$.

Solve: $y^{2} + 12 y + 36 = 32$.

Solve: $9 m^{2} - 12 m + 4 = 25$.

Solve: $16 n^{2} + 40 n + 25 = 4$.

Solve the following quadratic equations.

$a^{2} = 49$

Solve the following quadratic equations.

$r^{2} - 24 = 0$

Solve the following quadratic equations.

$u^{2} - 300 = 0$

Solve the following quadratic equations.

$4 m^{2} = 36$

Solve the following quadratic equations.

$x^{2} + 20 = 0$

Solve the following quadratic equations.

$\frac{2}{5} a^{2} + 3 = 11$

Solve the following quadratic equations.

$7 p^{2} + 10 = 26$

Solve the following quadratic equations.

$\left(x + 2\right)^{2} = 9$

Solve the following quadratic equations.

$\left(u - 6\right)^{2} = 64$

Solve the following quadratic equations.

$\left(m - 6\right)^{2} = 20$

Solve the following quadratic equations.

$\left(r - \frac{1}{2}\right)^{2} = \frac{3}{4}$

Solve the following quadratic equations.

$\left(a - 7\right)^{2} + 5 = 55$

Solve the following quadratic equations.

$\left(5 c + 1\right)^{2} = −27$

Solve the following quadratic equations.

$m^{2} - 4 m + 4 = 8$

Solve the following quadratic equations.

$25 x^{2} - 30 x + 9 = 36$

Solve using the Square Root Property.

$2 r^{2} = 32$

Solve using the Square Root Property.

$\left(a - 4\right)^{2} = 28$

Solve using the Square Root Property.

$9 w^{2} - 24 w + 16 = 1$

Solve using the Square Root Property.

$a^{2} - 18 = 0$

Solve using the Square Root Property.

$\left(p - \frac{1}{3}\right)^{2} = \frac{7}{9}$

Solve using the Square Root Property.

$m^{2} + 12 = 0$

Solve using the Square Root Property.

$u^{2} - 14 u + 49 = 72$

Solve using the Square Root Property.

$\left(m - 4\right)^{2} + 3 = 15$

Solve using the Square Root Property.

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

Solve using the Square Root Property.

$6 c^{2} + 4 = 29$

Solve using the Square Root Property.

$\left(x - 6\right)^{2} + 7 = 3$

Paola has enough mulch to cover 48 square feet. She wants to use it to make three square vegetable gardens of equal sizes. Solve the equation $3 s^{2} = 48$ to find $s$, the length of each garden side.

Explain why the equation $x^{2} + 12 = 8$ has no solution.