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Solve using the quadratic formula.\newliner2−4r−5=0r^2 - 4r - 5 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliner=r = _____ or r=r = _____

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Q. Solve using the quadratic formula.\newliner2−4r−5=0r^2 - 4r - 5 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliner=r = _____ or r=r = _____
  1. Write Quadratic Formula: Write down the quadratic formula.\newlineThe quadratic formula is used to solve equations of the form ax2+bx+c=0ax^2 + bx + c = 0. The formula is:\newliner=−b±b2−4ac2ar = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
  2. Identify Coefficients: Identify the coefficients aa, bb, and cc in the equation r2−4r−5=0r^2 − 4r − 5 = 0. Here, a=1a = 1, b=−4b = -4, and c=−5c = -5.
  3. Substitute into Formula: Substitute the coefficients into the quadratic formula.\newliner=−(−4)±(−4)2−4⋅1⋅(−5)2⋅1r = \frac{-(-4) \pm \sqrt{(-4)^2 - 4\cdot1\cdot(-5)}}{2\cdot1}\newliner=4±16+202r = \frac{4 \pm \sqrt{16 + 20}}{2}\newliner=4±362r = \frac{4 \pm \sqrt{36}}{2}
  4. Simplify Expression: Simplify the expression under the square root and then the entire formula.\newliner=4±362r = \frac{4 \pm \sqrt{36}}{2}\newliner=4±62r = \frac{4 \pm 6}{2}
  5. Solve for Values: Solve for the two possible values of rr.r=4+62r = \frac{4 + 6}{2} or r=4−62r = \frac{4 - 6}{2}r=102r = \frac{10}{2} or r=−22r = \frac{-2}{2}r=5r = 5 or r=−1r = -1

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