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Solve using the quadratic formula.\newline3q2+7q−6=03q^2 + 7q - 6 = 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.\newline3q2+7q−6=03q^2 + 7q - 6 = 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. Identify coefficients: Identify the coefficients aa, bb, and cc in the quadratic equation 3q2+7q−6=03q^2 + 7q - 6 = 0 by comparing it to the standard form ax2+bx+c=0ax^2 + bx + c = 0.a=3a = 3, b=7b = 7, c=−6c = -6
  2. Substitute values into formula: Substitute the values of aa, bb, and cc into the quadratic formula, q=−b±b2−4ac2aq = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.q=−(7)±(7)2−4(3)(−6)2(3)q = \frac{-(7) \pm \sqrt{(7)^2 - 4(3)(-6)}}{2(3)}
  3. Simplify discriminant: Simplify the expression under the square root, known as the discriminant. (7)2−4(3)(−6)=49+72=121\sqrt{(7)^2 - 4(3)(-6)} = \sqrt{49 + 72} = \sqrt{121}
  4. Calculate square root: Calculate the square root of the discriminant. 121=11\sqrt{121} = 11
  5. Substitute back into formula: Substitute the square root of the discriminant back into the quadratic formula.\newlineq=−7±112×3q = \frac{{-7 \pm 11}}{{2 \times 3}}
  6. Calculate possible solutions: Calculate the two possible solutions for qq.q=−7+116q = \frac{{-7 + 11}}{{6}} or q=−7−116q = \frac{{-7 - 11}}{{6}}q=46q = \frac{{4}}{{6}} or q=−186q = \frac{{-18}}{{6}}
  7. Simplify fractions: Simplify the fractions to their simplest form. q=23q = \frac{2}{3} or q=−3q = -3
  8. Round non-integer solution: If necessary, round the non-integer solution to the nearest hundredth. q=0.67q = 0.67 or q=−3q = -3

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