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Use the quadratic formula to solve. Express your answer in simplest form. 5r2+24r−3=25r^2 +24r-3= 2

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Quadratic equation with complex rootsright chevron icon

Full solution

Q. Use the quadratic formula to solve. Express your answer in simplest form. 5r2+24r−3=25r^2 +24r-3= 2
  1. Use Quadratic Formula: Now we'll use the quadratic formula, which is −b±b2−4ac2a\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Here, a=5a = 5, b=24b = 24, and c=−5c = -5.
  2. Plug Values: Plug the values into the quadratic formula.\newline(−24±242−4⋅5⋅(−5))/(2⋅5)(-24 \pm \sqrt{24^2 - 4 \cdot 5 \cdot (-5)}) / (2 \cdot 5)
  3. Simplify Square Root: Simplify inside the square root. −24±576+10010\frac{-24 \pm \sqrt{576 + 100}}{10}
  4. Add Numbers: Add the numbers under the square root.\newline(−24±67610)(\frac{-24 \pm \sqrt{676}}{10})
  5. Take Square Root: Take the square root of 676676.
    (−24±26)/10(-24 \pm 26) / 10
  6. Split Solutions: Split into two solutions.\newlineFirst solution: (−24+26)/10=2/10=1/5(-24 + 26) / 10 = 2 / 10 = 1/5\newlineSecond solution: (−24−26)/10=−50/10=−5(-24 - 26) / 10 = -50 / 10 = -5

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