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Simplifying 0 = -16t2 + 12t + 1500 Reorder the terms: 0 = 1500 + 12t + -16t2 Solving 0 = 1500 + 12t + -16t2 Solving for variable 't'. Combine like terms: 0 + -1500 = -1500 -1500 + -12t + 16t2 = 1500 + 12t + -16t2 + -1500 + -12t + 16t2 Reorder the terms: -1500 + -12t + 16t2 = 1500 + -1500 + 12t + -12t + -16t2 + 16t2 Combine like terms: 1500 + -1500 = 0 -1500 + -12t + 16t2 = 0 + 12t + -12t + -16t2 + 16t2 -1500 + -12t + 16t2 = 12t + -12t + -16t2 + 16t2 Combine like terms: 12t + -12t = 0 -1500 + -12t + 16t2 = 0 + -16t2 + 16t2 -1500 + -12t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -1500 + -12t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-375 + -3t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-375 + -3t + 4t2)' equal to zero and attempt to solve: Simplifying -375 + -3t + 4t2 = 0 Solving -375 + -3t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -93.75 + -0.75t + t2 = 0 Move the constant term to the right: Add '93.75' to each side of the equation. -93.75 + -0.75t + 93.75 + t2 = 0 + 93.75 Reorder the terms: -93.75 + 93.75 + -0.75t + t2 = 0 + 93.75 Combine like terms: -93.75 + 93.75 = 0.00 0.00 + -0.75t + t2 = 0 + 93.75 -0.75t + t2 = 0 + 93.75 Combine like terms: 0 + 93.75 = 93.75 -0.75t + t2 = 93.75 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 = 93.75 + 0.140625 Reorder the terms: 0.140625 + -0.75t + t2 = 93.75 + 0.140625 Combine like terms: 93.75 + 0.140625 = 93.890625 0.140625 + -0.75t + t2 = 93.890625 Factor a perfect square on the left side: (t + -0.375)(t + -0.375) = 93.890625 Calculate the square root of the right side: 9.689717488 Break this problem into two subproblems by setting (t + -0.375) equal to 9.689717488 and -9.689717488.Subproblem 1
t + -0.375 = 9.689717488 Simplifying t + -0.375 = 9.689717488 Reorder the terms: -0.375 + t = 9.689717488 Solving -0.375 + t = 9.689717488 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 = 9.689717488 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + t = 9.689717488 + 0.375 t = 9.689717488 + 0.375 Combine like terms: 9.689717488 + 0.375 = 10.064717488 t = 10.064717488 Simplifying t = 10.064717488Subproblem 2
t + -0.375 = -9.689717488 Simplifying t + -0.375 = -9.689717488 Reorder the terms: -0.375 + t = -9.689717488 Solving -0.375 + t = -9.689717488 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 = -9.689717488 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + t = -9.689717488 + 0.375 t = -9.689717488 + 0.375 Combine like terms: -9.689717488 + 0.375 = -9.314717488 t = -9.314717488 Simplifying t = -9.314717488Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.064717488, -9.314717488}Solution
t = {10.064717488, -9.314717488}
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