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Use the quadratic formula to solve. Express your answer in simplest form. 15q^(2)-14 q-8=0 Answer: q=

Use the quadratic formula to solve. Express your answer in simplest form.\newline15q2−14q−8=0 15 q^{2}-14 q-8=0 \newlineAnswer: q= q=

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Quadratic equation with complex rootsright chevron icon

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Q. Use the quadratic formula to solve. Express your answer in simplest form.\newline15q2−14q−8=0 15 q^{2}-14 q-8=0 \newlineAnswer: q= q=
  1. Identify coefficients: Identify the coefficients aa, bb, and cc in the quadratic equation 15q2−14q−8=015q^2 - 14q - 8 = 0. Compare 15q2−14q−815q^2 - 14q - 8 with the standard form ax2+bx+cax^2 + bx + c to find aa, bb, and cc. a=15a = 15, bb00, bb11
  2. Use quadratic formula: Use the quadratic formula to find the roots of the equation.\newlineThe quadratic formula is given by q=−b±b2−4ac2aq = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.\newlineSubstitute a=15a = 15, b=−14b = -14, and c=−8c = -8 into the formula.\newlineq=−(−14)±(−14)2−4⋅15⋅(−8)2⋅15q = \frac{-(-14) \pm \sqrt{(-14)^2 - 4 \cdot 15 \cdot (-8)}}{2 \cdot 15}
  3. Simplify terms in formula: Simplify the terms inside the square root.\newlineCalculate b2b^2 and 4ac4ac.\newline(−14)2=196(-14)^2 = 196\newline4×15×(−8)=−4804 \times 15 \times (-8) = -480\newlineNow, substitute these values into the square root.\newlineq=14±196−(−480)2×15q = \frac{14 \pm \sqrt{196 - (-480)}}{2 \times 15}
  4. Simplify expression under square root: Simplify the expression under the square root.\newlineCalculate 196−(−480)196 - (-480).\newline196−(−480)=196+480=676196 - (-480) = 196 + 480 = 676\newlineNow, substitute this value back into the equation.\newlineq=(14±676)/(2⋅15)q = (14 \pm \sqrt{676}) / (2\cdot15)
  5. Take square root of 676676: Take the square root of 676676.676=26\sqrt{676} = 26 Now, substitute this value back into the equation.q=(14±26)(2⋅15)q = \frac{(14 \pm 26)}{(2\cdot15)}
  6. Perform addition and subtraction: Simplify the equation by performing the addition and subtraction.\newlineCalculate the two possible values for qq.\newlineq=14+262×15q = \frac{14 + 26}{2\times15} and q=14−262×15q = \frac{14 - 26}{2\times15}\newlineq=4030q = \frac{40}{30} and q=−1230q = \frac{-12}{30}
  7. Simplify fractions: Simplify the fractions to get the roots in simplest form.\newlineDivide both the numerator and the denominator by their greatest common divisor.\newlineq=4030=43q = \frac{40}{30} = \frac{4}{3} and q=−1230=−25q = \frac{-12}{30} = \frac{-2}{5}

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