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Simplifying 140 + -8t + -16t2 = 0 Solving 140 + -8t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(35 + -2t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(35 + -2t + -4t2)' equal to zero and attempt to solve: Simplifying 35 + -2t + -4t2 = 0 Solving 35 + -2t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -8.75 + 0.5t + t2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + 0.5t + 8.75 + t2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + 0.5t + t2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + 0.5t + t2 = 0 + 8.75 0.5t + t2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 0.5t + t2 = 8.75 The t term is 0.5t. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5t + 0.0625 + t2 = 8.75 + 0.0625 Reorder the terms: 0.0625 + 0.5t + t2 = 8.75 + 0.0625 Combine like terms: 8.75 + 0.0625 = 8.8125 0.0625 + 0.5t + t2 = 8.8125 Factor a perfect square on the left side: (t + 0.25)(t + 0.25) = 8.8125 Calculate the square root of the right side: 2.968585522 Break this problem into two subproblems by setting (t + 0.25) equal to 2.968585522 and -2.968585522.Subproblem 1
t + 0.25 = 2.968585522 Simplifying t + 0.25 = 2.968585522 Reorder the terms: 0.25 + t = 2.968585522 Solving 0.25 + t = 2.968585522 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + t = 2.968585522 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + t = 2.968585522 + -0.25 t = 2.968585522 + -0.25 Combine like terms: 2.968585522 + -0.25 = 2.718585522 t = 2.718585522 Simplifying t = 2.718585522Subproblem 2
t + 0.25 = -2.968585522 Simplifying t + 0.25 = -2.968585522 Reorder the terms: 0.25 + t = -2.968585522 Solving 0.25 + t = -2.968585522 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + t = -2.968585522 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + t = -2.968585522 + -0.25 t = -2.968585522 + -0.25 Combine like terms: -2.968585522 + -0.25 = -3.218585522 t = -3.218585522 Simplifying t = -3.218585522Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.718585522, -3.218585522}Solution
t = {2.718585522, -3.218585522}
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