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Simplifying 12 = 160 + 12t + -16t2 Solving 12 = 160 + 12t + -16t2 Solving for variable 't'. Combine like terms: 12 + -160 = -148 -148 + -12t + 16t2 = 160 + 12t + -16t2 + -160 + -12t + 16t2 Reorder the terms: -148 + -12t + 16t2 = 160 + -160 + 12t + -12t + -16t2 + 16t2 Combine like terms: 160 + -160 = 0 -148 + -12t + 16t2 = 0 + 12t + -12t + -16t2 + 16t2 -148 + -12t + 16t2 = 12t + -12t + -16t2 + 16t2 Combine like terms: 12t + -12t = 0 -148 + -12t + 16t2 = 0 + -16t2 + 16t2 -148 + -12t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -148 + -12t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-37 + -3t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-37 + -3t + 4t2)' equal to zero and attempt to solve: Simplifying -37 + -3t + 4t2 = 0 Solving -37 + -3t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -9.25 + -0.75t + t2 = 0 Move the constant term to the right: Add '9.25' to each side of the equation. -9.25 + -0.75t + 9.25 + t2 = 0 + 9.25 Reorder the terms: -9.25 + 9.25 + -0.75t + t2 = 0 + 9.25 Combine like terms: -9.25 + 9.25 = 0.00 0.00 + -0.75t + t2 = 0 + 9.25 -0.75t + t2 = 0 + 9.25 Combine like terms: 0 + 9.25 = 9.25 -0.75t + t2 = 9.25 The t term is -0.75t. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75t + 0.140625 + t2 = 9.25 + 0.140625 Reorder the terms: 0.140625 + -0.75t + t2 = 9.25 + 0.140625 Combine like terms: 9.25 + 0.140625 = 9.390625 0.140625 + -0.75t + t2 = 9.390625 Factor a perfect square on the left side: (t + -0.375)(t + -0.375) = 9.390625 Calculate the square root of the right side: 3.064412668 Break this problem into two subproblems by setting (t + -0.375) equal to 3.064412668 and -3.064412668.Subproblem 1
t + -0.375 = 3.064412668 Simplifying t + -0.375 = 3.064412668 Reorder the terms: -0.375 + t = 3.064412668 Solving -0.375 + t = 3.064412668 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + t = 3.064412668 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + t = 3.064412668 + 0.375 t = 3.064412668 + 0.375 Combine like terms: 3.064412668 + 0.375 = 3.439412668 t = 3.439412668 Simplifying t = 3.439412668Subproblem 2
t + -0.375 = -3.064412668 Simplifying t + -0.375 = -3.064412668 Reorder the terms: -0.375 + t = -3.064412668 Solving -0.375 + t = -3.064412668 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + t = -3.064412668 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + t = -3.064412668 + 0.375 t = -3.064412668 + 0.375 Combine like terms: -3.064412668 + 0.375 = -2.689412668 t = -2.689412668 Simplifying t = -2.689412668Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.439412668, -2.689412668}Solution
t = {3.439412668, -2.689412668}
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