anonymous
  • anonymous
identify the solutions to the equation when you solve by completing the square
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
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Rogue
  • Rogue
\[x ^{2} - 5x = 24\] For a quadratic equation\[ax ^{2} + bx + c = 0\] When solving by completing the square, you must bring C to the other side first, which is already done for your equation. Next up must add \[\frac {b^{2}}{4}\] to both sides. In your case, \[\frac {b^{2}}{2} = \frac {-5^{2}}{2} = \frac {25}{2}\] Adding that do both sides of the equation, we get\[x ^{2} - 5x + \frac {25}{4} = 24 + \frac {25}{4}\] We see that we can factor this into:\[(x - \frac {5}{2})^{2} = 24 + \frac {25}{4} = \frac {121}{4}\] We can square root both sides to get\[(x-\frac {5}{2}) = \pm \sqrt{\frac {121}{4}}\] Now we just add 5/2 to both sides and we get that\[x = \frac {5}{2} \pm \sqrt{\frac {121}{4}}\] If we simplify that further, we get\[x = \frac {5}{2} \pm \frac {11}{2} = \frac {5 \pm 11}{2}\] The two solutions are then:\[x = \frac {5 + 11}{2} = 8\]\[x = \frac {5 - 11}{2} = -3\]

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