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Solve for tt.\newlinet2+2t−8=0t^2 + 2t - 8 = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlinet=t = ____

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Q. Solve for tt.\newlinet2+2t−8=0t^2 + 2t - 8 = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlinet=t = ____
  1. Identify the quadratic equation: Identify the quadratic equation to be solved.\newlineWe have the quadratic equation t2+2t−8=0t^2 + 2t - 8 = 0.
  2. Factor the quadratic equation: Factor the quadratic equation.\newlineWe need to find two numbers that multiply to −8-8 and add up to 22. The numbers 44 and −2-2 satisfy these conditions because 4×−2=−84 \times -2 = -8 and 4+(−2)=24 + (-2) = 2.\newlineSo we can write the equation as (t+4)(t−2)=0(t + 4)(t - 2) = 0.
  3. Solve for t: Solve for t using the zero product property.\newlineIf (t+4)(t−2)=0(t + 4)(t - 2) = 0, then either t+4=0t + 4 = 0 or t−2=0t - 2 = 0.\newlineFor t+4=0t + 4 = 0:\newlineSubtract 44 from both sides to solve for t.\newlinet+4−4=0−4t + 4 - 4 = 0 - 4\newlinet=−4t = -4
  4. Solve the second part: Solve the second part of the equation.\newlineFor t−2=0t - 2 = 0:\newlineAdd 22 to both sides to solve for tt.\newlinet−2+2=0+2t - 2 + 2 = 0 + 2\newlinet=2t = 2

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