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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