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Solve using the quadratic formula.\newline9t2−4t−9=09t^2 - 4t - 9 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinet=t = _____ or t=t = _____

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Q. Solve using the quadratic formula.\newline9t2−4t−9=09t^2 - 4t - 9 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinet=t = _____ or t=t = _____
  1. Identify values of aa, bb, cc: Identify the values of aa, bb, and cc in the quadratic equation 9t2−4t−9=09t^2 - 4t - 9 = 0. The quadratic equation is in the form at2+bt+c=0at^2 + bt + c = 0. For our equation, a=9a = 9, b=−4b = -4, and bb00.
  2. Substitute values into formula: Substitute the values of aa, bb, and cc into the quadratic formula t=−b±b2−4ac2at = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.\newlineSubstitute a=9a = 9, b=−4b = -4, and c=−9c = -9 into the formula.\newlinet=−(−4)±(−4)2−4⋅9⋅(−9)2⋅9t = \frac{-(-4) \pm \sqrt{(-4)^2 - 4\cdot9\cdot(-9)}}{2\cdot9}\newlinet=4±16+32418t = \frac{4 \pm \sqrt{16 + 324}}{18}
  3. Simplify expression and calculate discriminant: Simplify the expression under the square root and calculate the discriminant. (−4)2−4⋅9⋅(−9)=16+324=340\sqrt{(-4)^2 - 4\cdot 9\cdot (-9)} = \sqrt{16 + 324} = \sqrt{340}
  4. Calculate two possible solutions: Calculate the two possible solutions for tt.t=4±34018t = \frac{4 \pm \sqrt{340}}{18}t=4+34018t = \frac{4 + \sqrt{340}}{18} or t=4−34018t = \frac{4 - \sqrt{340}}{18}
  5. Simplify square root of 340340: Simplify the square root of 340340 to its decimal form and round to the nearest hundredth if necessary. 340\sqrt{340} is approximately 18.4418.44 when rounded to the nearest hundredth.
  6. Calculate approximate decimal values: Calculate the approximate decimal values of tt.t≈(4+18.44)/18t \approx (4 + 18.44) / 18 or t≈(4−18.44)/18t \approx (4 - 18.44) / 18t≈22.44/18t \approx 22.44 / 18 or t≈−14.44/18t \approx -14.44 / 18t≈1.25t \approx 1.25 or t≈−0.80t \approx -0.80

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