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Simplifying 0 = -4t2 + 15t + -12.5 Reorder the terms: 0 = -12.5 + 15t + -4t2 Solving 0 = -12.5 + 15t + -4t2 Solving for variable 't'. Combine like terms: 0 + 12.5 = 12.5 12.5 + -15t + 4t2 = -12.5 + 15t + -4t2 + 12.5 + -15t + 4t2 Reorder the terms: 12.5 + -15t + 4t2 = -12.5 + 12.5 + 15t + -15t + -4t2 + 4t2 Combine like terms: -12.5 + 12.5 = 0.0 12.5 + -15t + 4t2 = 0.0 + 15t + -15t + -4t2 + 4t2 12.5 + -15t + 4t2 = 15t + -15t + -4t2 + 4t2 Combine like terms: 15t + -15t = 0 12.5 + -15t + 4t2 = 0 + -4t2 + 4t2 12.5 + -15t + 4t2 = -4t2 + 4t2 Combine like terms: -4t2 + 4t2 = 0 12.5 + -15t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.125 + -3.75t + t2 = 0 Move the constant term to the right: Add '-3.125' to each side of the equation. 3.125 + -3.75t + -3.125 + t2 = 0 + -3.125 Reorder the terms: 3.125 + -3.125 + -3.75t + t2 = 0 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + -3.75t + t2 = 0 + -3.125 -3.75t + t2 = 0 + -3.125 Combine like terms: 0 + -3.125 = -3.125 -3.75t + t2 = -3.125 The t term is -3.75t. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75t + 3.515625 + t2 = -3.125 + 3.515625 Reorder the terms: 3.515625 + -3.75t + t2 = -3.125 + 3.515625 Combine like terms: -3.125 + 3.515625 = 0.390625 3.515625 + -3.75t + t2 = 0.390625 Factor a perfect square on the left side: (t + -1.875)(t + -1.875) = 0.390625 Calculate the square root of the right side: 0.625 Break this problem into two subproblems by setting (t + -1.875) equal to 0.625 and -0.625.Subproblem 1
t + -1.875 = 0.625 Simplifying t + -1.875 = 0.625 Reorder the terms: -1.875 + t = 0.625 Solving -1.875 + t = 0.625 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + t = 0.625 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = 0.625 + 1.875 t = 0.625 + 1.875 Combine like terms: 0.625 + 1.875 = 2.5 t = 2.5 Simplifying t = 2.5Subproblem 2
t + -1.875 = -0.625 Simplifying t + -1.875 = -0.625 Reorder the terms: -1.875 + t = -0.625 Solving -1.875 + t = -0.625 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + t = -0.625 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = -0.625 + 1.875 t = -0.625 + 1.875 Combine like terms: -0.625 + 1.875 = 1.25 t = 1.25 Simplifying t = 1.25Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.5, 1.25}
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