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Simplifying 0 = -16t2 + 156t + 116 Reorder the terms: 0 = 116 + 156t + -16t2 Solving 0 = 116 + 156t + -16t2 Solving for variable 't'. Combine like terms: 0 + -116 = -116 -116 + -156t + 16t2 = 116 + 156t + -16t2 + -116 + -156t + 16t2 Reorder the terms: -116 + -156t + 16t2 = 116 + -116 + 156t + -156t + -16t2 + 16t2 Combine like terms: 116 + -116 = 0 -116 + -156t + 16t2 = 0 + 156t + -156t + -16t2 + 16t2 -116 + -156t + 16t2 = 156t + -156t + -16t2 + 16t2 Combine like terms: 156t + -156t = 0 -116 + -156t + 16t2 = 0 + -16t2 + 16t2 -116 + -156t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -116 + -156t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-29 + -39t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-29 + -39t + 4t2)' equal to zero and attempt to solve: Simplifying -29 + -39t + 4t2 = 0 Solving -29 + -39t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -7.25 + -9.75t + t2 = 0 Move the constant term to the right: Add '7.25' to each side of the equation. -7.25 + -9.75t + 7.25 + t2 = 0 + 7.25 Reorder the terms: -7.25 + 7.25 + -9.75t + t2 = 0 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + -9.75t + t2 = 0 + 7.25 -9.75t + t2 = 0 + 7.25 Combine like terms: 0 + 7.25 = 7.25 -9.75t + t2 = 7.25 The t term is -9.75t. Take half its coefficient (-4.875). Square it (23.765625) and add it to both sides. Add '23.765625' to each side of the equation. -9.75t + 23.765625 + t2 = 7.25 + 23.765625 Reorder the terms: 23.765625 + -9.75t + t2 = 7.25 + 23.765625 Combine like terms: 7.25 + 23.765625 = 31.015625 23.765625 + -9.75t + t2 = 31.015625 Factor a perfect square on the left side: (t + -4.875)(t + -4.875) = 31.015625 Calculate the square root of the right side: 5.569167352 Break this problem into two subproblems by setting (t + -4.875) equal to 5.569167352 and -5.569167352.Subproblem 1
t + -4.875 = 5.569167352 Simplifying t + -4.875 = 5.569167352 Reorder the terms: -4.875 + t = 5.569167352 Solving -4.875 + t = 5.569167352 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + t = 5.569167352 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + t = 5.569167352 + 4.875 t = 5.569167352 + 4.875 Combine like terms: 5.569167352 + 4.875 = 10.444167352 t = 10.444167352 Simplifying t = 10.444167352Subproblem 2
t + -4.875 = -5.569167352 Simplifying t + -4.875 = -5.569167352 Reorder the terms: -4.875 + t = -5.569167352 Solving -4.875 + t = -5.569167352 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + t = -5.569167352 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + t = -5.569167352 + 4.875 t = -5.569167352 + 4.875 Combine like terms: -5.569167352 + 4.875 = -0.694167352 t = -0.694167352 Simplifying t = -0.694167352Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.444167352, -0.694167352}Solution
t = {10.444167352, -0.694167352}
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