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Simplifying 42 = -16t2 + 60t Reorder the terms: 42 = 60t + -16t2 Solving 42 = 60t + -16t2 Solving for variable 't'. Reorder the terms: 42 + -60t + 16t2 = 60t + -60t + -16t2 + 16t2 Combine like terms: 60t + -60t = 0 42 + -60t + 16t2 = 0 + -16t2 + 16t2 42 + -60t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 42 + -60t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(21 + -30t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(21 + -30t + 8t2)' equal to zero and attempt to solve: Simplifying 21 + -30t + 8t2 = 0 Solving 21 + -30t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 2.625 + -3.75t + t2 = 0 Move the constant term to the right: Add '-2.625' to each side of the equation. 2.625 + -3.75t + -2.625 + t2 = 0 + -2.625 Reorder the terms: 2.625 + -2.625 + -3.75t + t2 = 0 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + -3.75t + t2 = 0 + -2.625 -3.75t + t2 = 0 + -2.625 Combine like terms: 0 + -2.625 = -2.625 -3.75t + t2 = -2.625 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 = -2.625 + 3.515625 Reorder the terms: 3.515625 + -3.75t + t2 = -2.625 + 3.515625 Combine like terms: -2.625 + 3.515625 = 0.890625 3.515625 + -3.75t + t2 = 0.890625 Factor a perfect square on the left side: (t + -1.875)(t + -1.875) = 0.890625 Calculate the square root of the right side: 0.943729304 Break this problem into two subproblems by setting (t + -1.875) equal to 0.943729304 and -0.943729304.Subproblem 1
t + -1.875 = 0.943729304 Simplifying t + -1.875 = 0.943729304 Reorder the terms: -1.875 + t = 0.943729304 Solving -1.875 + t = 0.943729304 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 = 0.943729304 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = 0.943729304 + 1.875 t = 0.943729304 + 1.875 Combine like terms: 0.943729304 + 1.875 = 2.818729304 t = 2.818729304 Simplifying t = 2.818729304Subproblem 2
t + -1.875 = -0.943729304 Simplifying t + -1.875 = -0.943729304 Reorder the terms: -1.875 + t = -0.943729304 Solving -1.875 + t = -0.943729304 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 = -0.943729304 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + t = -0.943729304 + 1.875 t = -0.943729304 + 1.875 Combine like terms: -0.943729304 + 1.875 = 0.931270696 t = 0.931270696 Simplifying t = 0.931270696Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.818729304, 0.931270696}Solution
t = {2.818729304, 0.931270696}
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