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Simplifying -16t2 + 116t + 110 = 0 Reorder the terms: 110 + 116t + -16t2 = 0 Solving 110 + 116t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(55 + 58t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(55 + 58t + -8t2)' equal to zero and attempt to solve: Simplifying 55 + 58t + -8t2 = 0 Solving 55 + 58t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -6.875 + -7.25t + t2 = 0 Move the constant term to the right: Add '6.875' to each side of the equation. -6.875 + -7.25t + 6.875 + t2 = 0 + 6.875 Reorder the terms: -6.875 + 6.875 + -7.25t + t2 = 0 + 6.875 Combine like terms: -6.875 + 6.875 = 0.000 0.000 + -7.25t + t2 = 0 + 6.875 -7.25t + t2 = 0 + 6.875 Combine like terms: 0 + 6.875 = 6.875 -7.25t + t2 = 6.875 The t term is -7.25t. Take half its coefficient (-3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. -7.25t + 13.140625 + t2 = 6.875 + 13.140625 Reorder the terms: 13.140625 + -7.25t + t2 = 6.875 + 13.140625 Combine like terms: 6.875 + 13.140625 = 20.015625 13.140625 + -7.25t + t2 = 20.015625 Factor a perfect square on the left side: (t + -3.625)(t + -3.625) = 20.015625 Calculate the square root of the right side: 4.473882542 Break this problem into two subproblems by setting (t + -3.625) equal to 4.473882542 and -4.473882542.Subproblem 1
t + -3.625 = 4.473882542 Simplifying t + -3.625 = 4.473882542 Reorder the terms: -3.625 + t = 4.473882542 Solving -3.625 + t = 4.473882542 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + t = 4.473882542 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + t = 4.473882542 + 3.625 t = 4.473882542 + 3.625 Combine like terms: 4.473882542 + 3.625 = 8.098882542 t = 8.098882542 Simplifying t = 8.098882542Subproblem 2
t + -3.625 = -4.473882542 Simplifying t + -3.625 = -4.473882542 Reorder the terms: -3.625 + t = -4.473882542 Solving -3.625 + t = -4.473882542 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + t = -4.473882542 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + t = -4.473882542 + 3.625 t = -4.473882542 + 3.625 Combine like terms: -4.473882542 + 3.625 = -0.848882542 t = -0.848882542 Simplifying t = -0.848882542Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.098882542, -0.848882542}Solution
t = {8.098882542, -0.848882542}
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