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Solve using the quadratic formula.\newlineq2−9q+8=0q^2 - 9q + 8 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineq=q = _____ or q=q = _____

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Q. Solve using the quadratic formula.\newlineq2−9q+8=0q^2 - 9q + 8 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineq=q = _____ or q=q = _____
  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 given by:\newlineq=−b±b2−4ac2aq = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\newlineIn our equation, a=1a = 1, b=−9b = -9, and c=8c = 8.
  2. Substitute Values: Substitute the values of aa, bb, and cc into the quadratic formula.\newlineq=−(−9)±(−9)2−4(1)(8)2(1)q = \frac{-(-9) \pm \sqrt{(-9)^2 - 4(1)(8)}}{2(1)}\newlineq=9±81−322q = \frac{9 \pm \sqrt{81 - 32}}{2}\newlineq=9±492q = \frac{9 \pm \sqrt{49}}{2}
  3. Simplify Equation: Simplify the square root and the equation.\newline49\sqrt{49} is 77, so we have:\newlineq=(9±7)/2q = (9 \pm 7) / 2\newlineThis gives us two possible solutions for qq.
  4. Solve for Solutions: Solve for the two possible values of qq.\newlineFirst solution:\newlineq=(9+7)/2q = (9 + 7) / 2\newlineq=16/2q = 16 / 2\newlineq=8q = 8\newlineSecond solution:\newlineq=(9−7)/2q = (9 - 7) / 2\newlineq=2/2q = 2 / 2\newlineq=1q = 1

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