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Simplifying 110(t) = -16t2 + 110 Reorder the terms: 110t = 110 + -16t2 Solving 110t = 110 + -16t2 Solving for variable 't'. Reorder the terms: -110 + 110t + 16t2 = 110 + -16t2 + -110 + 16t2 Reorder the terms: -110 + 110t + 16t2 = 110 + -110 + -16t2 + 16t2 Combine like terms: 110 + -110 = 0 -110 + 110t + 16t2 = 0 + -16t2 + 16t2 -110 + 110t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -110 + 110t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-55 + 55t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-55 + 55t + 8t2)' equal to zero and attempt to solve: Simplifying -55 + 55t + 8t2 = 0 Solving -55 + 55t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -6.875 + 6.875t + t2 = 0 Move the constant term to the right: Add '6.875' to each side of the equation. -6.875 + 6.875t + 6.875 + t2 = 0 + 6.875 Reorder the terms: -6.875 + 6.875 + 6.875t + t2 = 0 + 6.875 Combine like terms: -6.875 + 6.875 = 0.000 0.000 + 6.875t + t2 = 0 + 6.875 6.875t + t2 = 0 + 6.875 Combine like terms: 0 + 6.875 = 6.875 6.875t + t2 = 6.875 The t term is 6.875t. Take half its coefficient (3.4375). Square it (11.81640625) and add it to both sides. Add '11.81640625' to each side of the equation. 6.875t + 11.81640625 + t2 = 6.875 + 11.81640625 Reorder the terms: 11.81640625 + 6.875t + t2 = 6.875 + 11.81640625 Combine like terms: 6.875 + 11.81640625 = 18.69140625 11.81640625 + 6.875t + t2 = 18.69140625 Factor a perfect square on the left side: (t + 3.4375)(t + 3.4375) = 18.69140625 Calculate the square root of the right side: 4.323355901 Break this problem into two subproblems by setting (t + 3.4375) equal to 4.323355901 and -4.323355901.Subproblem 1
t + 3.4375 = 4.323355901 Simplifying t + 3.4375 = 4.323355901 Reorder the terms: 3.4375 + t = 4.323355901 Solving 3.4375 + t = 4.323355901 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.4375' to each side of the equation. 3.4375 + -3.4375 + t = 4.323355901 + -3.4375 Combine like terms: 3.4375 + -3.4375 = 0.0000 0.0000 + t = 4.323355901 + -3.4375 t = 4.323355901 + -3.4375 Combine like terms: 4.323355901 + -3.4375 = 0.885855901 t = 0.885855901 Simplifying t = 0.885855901Subproblem 2
t + 3.4375 = -4.323355901 Simplifying t + 3.4375 = -4.323355901 Reorder the terms: 3.4375 + t = -4.323355901 Solving 3.4375 + t = -4.323355901 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.4375' to each side of the equation. 3.4375 + -3.4375 + t = -4.323355901 + -3.4375 Combine like terms: 3.4375 + -3.4375 = 0.0000 0.0000 + t = -4.323355901 + -3.4375 t = -4.323355901 + -3.4375 Combine like terms: -4.323355901 + -3.4375 = -7.760855901 t = -7.760855901 Simplifying t = -7.760855901Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.885855901, -7.760855901}Solution
t = {0.885855901, -7.760855901}
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