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Simplifying -16t2 + 12t + 1300 = 0 Reorder the terms: 1300 + 12t + -16t2 = 0 Solving 1300 + 12t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(325 + 3t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(325 + 3t + -4t2)' equal to zero and attempt to solve: Simplifying 325 + 3t + -4t2 = 0 Solving 325 + 3t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -81.25 + -0.75t + t2 = 0 Move the constant term to the right: Add '81.25' to each side of the equation. -81.25 + -0.75t + 81.25 + t2 = 0 + 81.25 Reorder the terms: -81.25 + 81.25 + -0.75t + t2 = 0 + 81.25 Combine like terms: -81.25 + 81.25 = 0.00 0.00 + -0.75t + t2 = 0 + 81.25 -0.75t + t2 = 0 + 81.25 Combine like terms: 0 + 81.25 = 81.25 -0.75t + t2 = 81.25 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 = 81.25 + 0.140625 Reorder the terms: 0.140625 + -0.75t + t2 = 81.25 + 0.140625 Combine like terms: 81.25 + 0.140625 = 81.390625 0.140625 + -0.75t + t2 = 81.390625 Factor a perfect square on the left side: (t + -0.375)(t + -0.375) = 81.390625 Calculate the square root of the right side: 9.021675288 Break this problem into two subproblems by setting (t + -0.375) equal to 9.021675288 and -9.021675288.Subproblem 1
t + -0.375 = 9.021675288 Simplifying t + -0.375 = 9.021675288 Reorder the terms: -0.375 + t = 9.021675288 Solving -0.375 + t = 9.021675288 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 = 9.021675288 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + t = 9.021675288 + 0.375 t = 9.021675288 + 0.375 Combine like terms: 9.021675288 + 0.375 = 9.396675288 t = 9.396675288 Simplifying t = 9.396675288Subproblem 2
t + -0.375 = -9.021675288 Simplifying t + -0.375 = -9.021675288 Reorder the terms: -0.375 + t = -9.021675288 Solving -0.375 + t = -9.021675288 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 = -9.021675288 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + t = -9.021675288 + 0.375 t = -9.021675288 + 0.375 Combine like terms: -9.021675288 + 0.375 = -8.646675288 t = -8.646675288 Simplifying t = -8.646675288Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.396675288, -8.646675288}Solution
t = {9.396675288, -8.646675288}
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