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Simplifying 0 = -16t2 + -18t + 110 Reorder the terms: 0 = 110 + -18t + -16t2 Solving 0 = 110 + -18t + -16t2 Solving for variable 't'. Combine like terms: 0 + -110 = -110 -110 + 18t + 16t2 = 110 + -18t + -16t2 + -110 + 18t + 16t2 Reorder the terms: -110 + 18t + 16t2 = 110 + -110 + -18t + 18t + -16t2 + 16t2 Combine like terms: 110 + -110 = 0 -110 + 18t + 16t2 = 0 + -18t + 18t + -16t2 + 16t2 -110 + 18t + 16t2 = -18t + 18t + -16t2 + 16t2 Combine like terms: -18t + 18t = 0 -110 + 18t + 16t2 = 0 + -16t2 + 16t2 -110 + 18t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -110 + 18t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-55 + 9t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-55 + 9t + 8t2)' equal to zero and attempt to solve: Simplifying -55 + 9t + 8t2 = 0 Solving -55 + 9t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -6.875 + 1.125t + t2 = 0 Move the constant term to the right: Add '6.875' to each side of the equation. -6.875 + 1.125t + 6.875 + t2 = 0 + 6.875 Reorder the terms: -6.875 + 6.875 + 1.125t + t2 = 0 + 6.875 Combine like terms: -6.875 + 6.875 = 0.000 0.000 + 1.125t + t2 = 0 + 6.875 1.125t + t2 = 0 + 6.875 Combine like terms: 0 + 6.875 = 6.875 1.125t + t2 = 6.875 The t term is 1.125t. Take half its coefficient (0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. 1.125t + 0.31640625 + t2 = 6.875 + 0.31640625 Reorder the terms: 0.31640625 + 1.125t + t2 = 6.875 + 0.31640625 Combine like terms: 6.875 + 0.31640625 = 7.19140625 0.31640625 + 1.125t + t2 = 7.19140625 Factor a perfect square on the left side: (t + 0.5625)(t + 0.5625) = 7.19140625 Calculate the square root of the right side: 2.681679744 Break this problem into two subproblems by setting (t + 0.5625) equal to 2.681679744 and -2.681679744.Subproblem 1
t + 0.5625 = 2.681679744 Simplifying t + 0.5625 = 2.681679744 Reorder the terms: 0.5625 + t = 2.681679744 Solving 0.5625 + t = 2.681679744 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + t = 2.681679744 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + t = 2.681679744 + -0.5625 t = 2.681679744 + -0.5625 Combine like terms: 2.681679744 + -0.5625 = 2.119179744 t = 2.119179744 Simplifying t = 2.119179744Subproblem 2
t + 0.5625 = -2.681679744 Simplifying t + 0.5625 = -2.681679744 Reorder the terms: 0.5625 + t = -2.681679744 Solving 0.5625 + t = -2.681679744 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + t = -2.681679744 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + t = -2.681679744 + -0.5625 t = -2.681679744 + -0.5625 Combine like terms: -2.681679744 + -0.5625 = -3.244179744 t = -3.244179744 Simplifying t = -3.244179744Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.119179744, -3.244179744}Solution
t = {2.119179744, -3.244179744}
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