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Solve using the quadratic formula.\newline4t2+4t+1=04t^2 + 4t + 1 = 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+1=04t^2 + 4t + 1 = 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+1=04t^2 + 4t + 1 = 0.\newlineThe quadratic equation is in the form at2+bt+c=0at^2 + bt + c = 0, so by comparison:\newlinea=4a = 4\newlineb=4b = 4\newlinec=1c = 1
  2. Substitute values: 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}. t=−(4)±(4)2−4⋅4⋅12⋅4t = \frac{-(4) \pm \sqrt{(4)^2 - 4\cdot4\cdot1}}{2\cdot4}
  3. Simplify discriminant: Simplify the expression under the square root (the discriminant). (4)2−4⋅4⋅1=16−16=0\sqrt{(4)^2 - 4\cdot 4\cdot 1} = \sqrt{16 - 16} = \sqrt{0}
  4. Continue simplifying: Continue simplifying the quadratic formula with the values found.\newlinet=−4±08t = \frac{-4 \pm \sqrt{0}}{8}\newlineSince 0=0\sqrt{0} = 0, the equation simplifies to:\newlinet=−4±08t = \frac{-4 \pm 0}{8}
  5. Solve for tt: Solve for the two possible values of tt.t=(−4+0)/8t = (-4 + 0) / 8 or t=(−4−0)/8t = (-4 - 0) / 8Both expressions simplify to the same value since adding or subtracting zero does not change the value.t=−4/8t = -4 / 8t=−1/2t = -1/2

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