# POLQ 2 | Solutions (Solving Quadratic Equations)

Solution strategies shown algebraically:

1) $$x^2 + 2x =7$$

$$x^2 + 2x + 1 =7+1$$

$$(x+1)^2 =8$$

$$x+1 = \pm \sqrt{8}$$

$$x = -1 \pm 2\sqrt{2}$$

2) $$x^2 – 3x =8$$

$$x^2 – 3x + \Large \frac{9}{4} \normalsize = 8 + \Large \frac{9}{4}$$

$$(x- \Large \frac{3}{2} \normalsize )^2 = 10 \Large \frac{1}{4}$$

$$x- \Large \frac{3}{2} \normalsize = \pm \sqrt{10\Large \frac{1}{4}}$$

$$x = \Large \frac{3}{2} \normalsize \pm \sqrt{10\Large \frac{1}{4}}$$

3) $$x^2 – 6x =4$$

$$x^2 – 6x + 9 = 9+4$$

$$(x-3)^2 = 9 +4$$

$$x-3 = \pm \sqrt{13}$$

$$x = 3 \pm \sqrt{13}$$

Solutions with the formula: Note the solutions are the same

1. a = 1, b = 2 and c = -7 ;  $$x = \Large\frac{-2\pm\sqrt{4 +28}}{2}$$ simplify

2. a = 1, b = -3 and c = -8;  $$x = \Large\frac{3\pm\sqrt{9 +32}}{2}$$  simplify

3. a = 1, b = -6 and c =-4; $$x = \Large\frac{6\pm\sqrt{36 +16}}{2}$$ simplify