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Simplifying 40t + -5t2 + -15 = 0 Reorder the terms: -15 + 40t + -5t2 = 0 Solving -15 + 40t + -5t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(-3 + 8t + -1t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3 + 8t + -1t2)' equal to zero and attempt to solve: Simplifying -3 + 8t + -1t2 = 0 Solving -3 + 8t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 3 + -8t + t2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -8t + -3 + t2 = 0 + -3 Reorder the terms: 3 + -3 + -8t + t2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8t + t2 = 0 + -3 -8t + t2 = 0 + -3 Combine like terms: 0 + -3 = -3 -8t + t2 = -3 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = -3 + 16 Reorder the terms: 16 + -8t + t2 = -3 + 16 Combine like terms: -3 + 16 = 13 16 + -8t + t2 = 13 Factor a perfect square on the left side: (t + -4)(t + -4) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (t + -4) equal to 3.605551275 and -3.605551275.Subproblem 1
t + -4 = 3.605551275 Simplifying t + -4 = 3.605551275 Reorder the terms: -4 + t = 3.605551275 Solving -4 + t = 3.605551275 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 3.605551275 + 4 Combine like terms: -4 + 4 = 0 0 + t = 3.605551275 + 4 t = 3.605551275 + 4 Combine like terms: 3.605551275 + 4 = 7.605551275 t = 7.605551275 Simplifying t = 7.605551275Subproblem 2
t + -4 = -3.605551275 Simplifying t + -4 = -3.605551275 Reorder the terms: -4 + t = -3.605551275 Solving -4 + t = -3.605551275 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -3.605551275 + 4 Combine like terms: -4 + 4 = 0 0 + t = -3.605551275 + 4 t = -3.605551275 + 4 Combine like terms: -3.605551275 + 4 = 0.394448725 t = 0.394448725 Simplifying t = 0.394448725Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.605551275, 0.394448725}Solution
t = {7.605551275, 0.394448725}
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