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Simplifying -6t2 + 72t + 40 = 0 Reorder the terms: 40 + 72t + -6t2 = 0 Solving 40 + 72t + -6t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(20 + 36t + -3t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(20 + 36t + -3t2)' equal to zero and attempt to solve: Simplifying 20 + 36t + -3t2 = 0 Solving 20 + 36t + -3t2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -6.666666667 + -12t + t2 = 0 Move the constant term to the right: Add '6.666666667' to each side of the equation. -6.666666667 + -12t + 6.666666667 + t2 = 0 + 6.666666667 Reorder the terms: -6.666666667 + 6.666666667 + -12t + t2 = 0 + 6.666666667 Combine like terms: -6.666666667 + 6.666666667 = 0.000000000 0.000000000 + -12t + t2 = 0 + 6.666666667 -12t + t2 = 0 + 6.666666667 Combine like terms: 0 + 6.666666667 = 6.666666667 -12t + t2 = 6.666666667 The t term is -12t. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12t + 36 + t2 = 6.666666667 + 36 Reorder the terms: 36 + -12t + t2 = 6.666666667 + 36 Combine like terms: 6.666666667 + 36 = 42.666666667 36 + -12t + t2 = 42.666666667 Factor a perfect square on the left side: (t + -6)(t + -6) = 42.666666667 Calculate the square root of the right side: 6.531972647 Break this problem into two subproblems by setting (t + -6) equal to 6.531972647 and -6.531972647.Subproblem 1
t + -6 = 6.531972647 Simplifying t + -6 = 6.531972647 Reorder the terms: -6 + t = 6.531972647 Solving -6 + t = 6.531972647 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = 6.531972647 + 6 Combine like terms: -6 + 6 = 0 0 + t = 6.531972647 + 6 t = 6.531972647 + 6 Combine like terms: 6.531972647 + 6 = 12.531972647 t = 12.531972647 Simplifying t = 12.531972647Subproblem 2
t + -6 = -6.531972647 Simplifying t + -6 = -6.531972647 Reorder the terms: -6 + t = -6.531972647 Solving -6 + t = -6.531972647 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = -6.531972647 + 6 Combine like terms: -6 + 6 = 0 0 + t = -6.531972647 + 6 t = -6.531972647 + 6 Combine like terms: -6.531972647 + 6 = -0.531972647 t = -0.531972647 Simplifying t = -0.531972647Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.531972647, -0.531972647}Solution
t = {12.531972647, -0.531972647}
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