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Simplifying 0 = -16t2 + 12t + 90 Reorder the terms: 0 = 90 + 12t + -16t2 Solving 0 = 90 + 12t + -16t2 Solving for variable 't'. Combine like terms: 0 + -90 = -90 -90 + -12t + 16t2 = 90 + 12t + -16t2 + -90 + -12t + 16t2 Reorder the terms: -90 + -12t + 16t2 = 90 + -90 + 12t + -12t + -16t2 + 16t2 Combine like terms: 90 + -90 = 0 -90 + -12t + 16t2 = 0 + 12t + -12t + -16t2 + 16t2 -90 + -12t + 16t2 = 12t + -12t + -16t2 + 16t2 Combine like terms: 12t + -12t = 0 -90 + -12t + 16t2 = 0 + -16t2 + 16t2 -90 + -12t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -90 + -12t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-45 + -6t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-45 + -6t + 8t2)' equal to zero and attempt to solve: Simplifying -45 + -6t + 8t2 = 0 Solving -45 + -6t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -5.625 + -0.75t + t2 = 0 Move the constant term to the right: Add '5.625' to each side of the equation. -5.625 + -0.75t + 5.625 + t2 = 0 + 5.625 Reorder the terms: -5.625 + 5.625 + -0.75t + t2 = 0 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + -0.75t + t2 = 0 + 5.625 -0.75t + t2 = 0 + 5.625 Combine like terms: 0 + 5.625 = 5.625 -0.75t + t2 = 5.625 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 = 5.625 + 0.140625 Reorder the terms: 0.140625 + -0.75t + t2 = 5.625 + 0.140625 Combine like terms: 5.625 + 0.140625 = 5.765625 0.140625 + -0.75t + t2 = 5.765625 Factor a perfect square on the left side: (t + -0.375)(t + -0.375) = 5.765625 Calculate the square root of the right side: 2.401171589 Break this problem into two subproblems by setting (t + -0.375) equal to 2.401171589 and -2.401171589.Subproblem 1
t + -0.375 = 2.401171589 Simplifying t + -0.375 = 2.401171589 Reorder the terms: -0.375 + t = 2.401171589 Solving -0.375 + t = 2.401171589 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 = 2.401171589 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + t = 2.401171589 + 0.375 t = 2.401171589 + 0.375 Combine like terms: 2.401171589 + 0.375 = 2.776171589 t = 2.776171589 Simplifying t = 2.776171589Subproblem 2
t + -0.375 = -2.401171589 Simplifying t + -0.375 = -2.401171589 Reorder the terms: -0.375 + t = -2.401171589 Solving -0.375 + t = -2.401171589 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 = -2.401171589 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + t = -2.401171589 + 0.375 t = -2.401171589 + 0.375 Combine like terms: -2.401171589 + 0.375 = -2.026171589 t = -2.026171589 Simplifying t = -2.026171589Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.776171589, -2.026171589}Solution
t = {2.776171589, -2.026171589}
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