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Simplifying -16t2 + 135t + 76 = 0 Reorder the terms: 76 + 135t + -16t2 = 0 Solving 76 + 135t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -4.75 + -8.4375t + t2 = 0 Move the constant term to the right: Add '4.75' to each side of the equation. -4.75 + -8.4375t + 4.75 + t2 = 0 + 4.75 Reorder the terms: -4.75 + 4.75 + -8.4375t + t2 = 0 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + -8.4375t + t2 = 0 + 4.75 -8.4375t + t2 = 0 + 4.75 Combine like terms: 0 + 4.75 = 4.75 -8.4375t + t2 = 4.75 The t term is -8.4375t. Take half its coefficient (-4.21875). Square it (17.79785156) and add it to both sides. Add '17.79785156' to each side of the equation. -8.4375t + 17.79785156 + t2 = 4.75 + 17.79785156 Reorder the terms: 17.79785156 + -8.4375t + t2 = 4.75 + 17.79785156 Combine like terms: 4.75 + 17.79785156 = 22.54785156 17.79785156 + -8.4375t + t2 = 22.54785156 Factor a perfect square on the left side: (t + -4.21875)(t + -4.21875) = 22.54785156 Calculate the square root of the right side: 4.748457809 Break this problem into two subproblems by setting (t + -4.21875) equal to 4.748457809 and -4.748457809.Subproblem 1
t + -4.21875 = 4.748457809 Simplifying t + -4.21875 = 4.748457809 Reorder the terms: -4.21875 + t = 4.748457809 Solving -4.21875 + t = 4.748457809 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.21875' to each side of the equation. -4.21875 + 4.21875 + t = 4.748457809 + 4.21875 Combine like terms: -4.21875 + 4.21875 = 0.00000 0.00000 + t = 4.748457809 + 4.21875 t = 4.748457809 + 4.21875 Combine like terms: 4.748457809 + 4.21875 = 8.967207809 t = 8.967207809 Simplifying t = 8.967207809Subproblem 2
t + -4.21875 = -4.748457809 Simplifying t + -4.21875 = -4.748457809 Reorder the terms: -4.21875 + t = -4.748457809 Solving -4.21875 + t = -4.748457809 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.21875' to each side of the equation. -4.21875 + 4.21875 + t = -4.748457809 + 4.21875 Combine like terms: -4.21875 + 4.21875 = 0.00000 0.00000 + t = -4.748457809 + 4.21875 t = -4.748457809 + 4.21875 Combine like terms: -4.748457809 + 4.21875 = -0.529707809 t = -0.529707809 Simplifying t = -0.529707809Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.967207809, -0.529707809}
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