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

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