POLQ 2 | Practice (Solving Quadratic Equations) Solutions

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) \(x^2-3x =8\)

\(x^2-3x+\dfrac{9}{4} = 8+\dfrac{9}{4}\)

\((x-\dfrac{3}{2})^2 = 10 \dfrac{1}{4}\)

\(x-\dfrac{3}{2}= \pm \sqrt{10\dfrac{1}{4}}\)

\(x = \dfrac{3}{2}\pm \sqrt{10\dfrac{1}{4}}\)

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 \(c = -7\);  \(x = \dfrac{-2\pm\sqrt{4+28}}{2}\) simplify

2. \(a = 1, b = -3\) and \(c = -8\);  \(x = \dfrac{3\pm\sqrt{9+32}}{2}\)  simplify

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


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