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Simplifying 4t2 + 48t = 160 Reorder the terms: 48t + 4t2 = 160 Solving 48t + 4t2 = 160 Solving for variable 't'. Reorder the terms: -160 + 48t + 4t2 = 160 + -160 Combine like terms: 160 + -160 = 0 -160 + 48t + 4t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-40 + 12t + t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-40 + 12t + t2)' equal to zero and attempt to solve: Simplifying -40 + 12t + t2 = 0 Solving -40 + 12t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + 12t + 40 + t2 = 0 + 40 Reorder the terms: -40 + 40 + 12t + t2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 12t + t2 = 0 + 40 12t + t2 = 0 + 40 Combine like terms: 0 + 40 = 40 12t + t2 = 40 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 = 40 + 36 Reorder the terms: 36 + 12t + t2 = 40 + 36 Combine like terms: 40 + 36 = 76 36 + 12t + t2 = 76 Factor a perfect square on the left side: (t + 6)(t + 6) = 76 Calculate the square root of the right side: 8.717797887 Break this problem into two subproblems by setting (t + 6) equal to 8.717797887 and -8.717797887.Subproblem 1
t + 6 = 8.717797887 Simplifying t + 6 = 8.717797887 Reorder the terms: 6 + t = 8.717797887 Solving 6 + t = 8.717797887 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 = 8.717797887 + -6 Combine like terms: 6 + -6 = 0 0 + t = 8.717797887 + -6 t = 8.717797887 + -6 Combine like terms: 8.717797887 + -6 = 2.717797887 t = 2.717797887 Simplifying t = 2.717797887Subproblem 2
t + 6 = -8.717797887 Simplifying t + 6 = -8.717797887 Reorder the terms: 6 + t = -8.717797887 Solving 6 + t = -8.717797887 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 = -8.717797887 + -6 Combine like terms: 6 + -6 = 0 0 + t = -8.717797887 + -6 t = -8.717797887 + -6 Combine like terms: -8.717797887 + -6 = -14.717797887 t = -14.717797887 Simplifying t = -14.717797887Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.717797887, -14.717797887}Solution
t = {2.717797887, -14.717797887}
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