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Simplifying -16t2 + 60t + 310 = 0 Reorder the terms: 310 + 60t + -16t2 = 0 Solving 310 + 60t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(155 + 30t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(155 + 30t + -8t2)' equal to zero and attempt to solve: Simplifying 155 + 30t + -8t2 = 0 Solving 155 + 30t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -19.375 + -3.75t + t2 = 0 Move the constant term to the right: Add '19.375' to each side of the equation. -19.375 + -3.75t + 19.375 + t2 = 0 + 19.375 Reorder the terms: -19.375 + 19.375 + -3.75t + t2 = 0 + 19.375 Combine like terms: -19.375 + 19.375 = 0.000 0.000 + -3.75t + t2 = 0 + 19.375 -3.75t + t2 = 0 + 19.375 Combine like terms: 0 + 19.375 = 19.375 -3.75t + t2 = 19.375 The t term is -3.75t. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75t + 3.515625 + t2 = 19.375 + 3.515625 Reorder the terms: 3.515625 + -3.75t + t2 = 19.375 + 3.515625 Combine like terms: 19.375 + 3.515625 = 22.890625 3.515625 + -3.75t + t2 = 22.890625 Factor a perfect square on the left side: (t + -1.875)(t + -1.875) = 22.890625 Calculate the square root of the right side: 4.784414802 Break this problem into two subproblems by setting (t + -1.875) equal to 4.784414802 and -4.784414802.Subproblem 1
t + -1.875 = 4.784414802 Simplifying t + -1.875 = 4.784414802 Reorder the terms: -1.875 + t = 4.784414802 Solving -1.875 + t = 4.784414802 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + t = 4.784414802 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = 4.784414802 + 1.875 t = 4.784414802 + 1.875 Combine like terms: 4.784414802 + 1.875 = 6.659414802 t = 6.659414802 Simplifying t = 6.659414802Subproblem 2
t + -1.875 = -4.784414802 Simplifying t + -1.875 = -4.784414802 Reorder the terms: -1.875 + t = -4.784414802 Solving -1.875 + t = -4.784414802 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + t = -4.784414802 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = -4.784414802 + 1.875 t = -4.784414802 + 1.875 Combine like terms: -4.784414802 + 1.875 = -2.909414802 t = -2.909414802 Simplifying t = -2.909414802Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.659414802, -2.909414802}Solution
t = {6.659414802, -2.909414802}
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