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Solve using the quadratic formula.\newline4t2+4t−3=04t^2 + 4t - 3 = 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.\newline4t2+4t−3=04t^2 + 4t - 3 = 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: Identify the values of aa, bb, and cc in the quadratic equation 4t2+4t−3=04t^2 + 4t - 3 = 0. The quadratic equation is in the form at2+bt+c=0at^2 + bt + c = 0, so by comparison: a=4a = 4 b=4b = 4 c=−3c = -3
  2. Substitute in formula: Substitute the values of aa, bb, and cc into the quadratic formula to find tt. The quadratic formula is t=−b±b2−4ac2at = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. So we have: t=−(4)±(4)2−4⋅4⋅(−3)2⋅4t = \frac{-(4) \pm \sqrt{(4)^2 - 4\cdot4\cdot(-3)}}{2\cdot4}
  3. Simplify discriminant: Simplify the expression under the square root (the discriminant). (4)2−4⋅4⋅(−3)=16+48=64\sqrt{(4)^2 - 4\cdot 4\cdot (-3)} = \sqrt{16 + 48} = \sqrt{64}
  4. Continue simplifying: Continue simplifying the quadratic formula with the calculated discriminant.\newlinet=−4±648t = \frac{-4 \pm \sqrt{64}}{8}\newlinet=−4±88t = \frac{-4 \pm 8}{8}
  5. Find possible values: Find the two possible values for tt.t=($−4t = (\$-4 + 88) / 88\) or t=($−4t = (\$-4 - 88) / 88\)t=$4t = \$4 / 88\) or t=$−12t = \$-12 / 88\)
  6. Simplify fractions: Simplify the fractions to get the final answers.\newlinet=12t = \frac{1}{2} or t=−32t = -\frac{3}{2}\newlineIf we want to express these as decimals rounded to the nearest hundredth:\newlinet≈0.50t \approx 0.50 or t≈−1.50t \approx -1.50

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