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Simplifying 58 = -16t2 + 68t Reorder the terms: 58 = 68t + -16t2 Solving 58 = 68t + -16t2 Solving for variable 't'. Reorder the terms: 58 + -68t + 16t2 = 68t + -68t + -16t2 + 16t2 Combine like terms: 68t + -68t = 0 58 + -68t + 16t2 = 0 + -16t2 + 16t2 58 + -68t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 58 + -68t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(29 + -34t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(29 + -34t + 8t2)' equal to zero and attempt to solve: Simplifying 29 + -34t + 8t2 = 0 Solving 29 + -34t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 3.625 + -4.25t + t2 = 0 Move the constant term to the right: Add '-3.625' to each side of the equation. 3.625 + -4.25t + -3.625 + t2 = 0 + -3.625 Reorder the terms: 3.625 + -3.625 + -4.25t + t2 = 0 + -3.625 Combine like terms: 3.625 + -3.625 = 0.000 0.000 + -4.25t + t2 = 0 + -3.625 -4.25t + t2 = 0 + -3.625 Combine like terms: 0 + -3.625 = -3.625 -4.25t + t2 = -3.625 The t term is -4.25t. Take half its coefficient (-2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. -4.25t + 4.515625 + t2 = -3.625 + 4.515625 Reorder the terms: 4.515625 + -4.25t + t2 = -3.625 + 4.515625 Combine like terms: -3.625 + 4.515625 = 0.890625 4.515625 + -4.25t + t2 = 0.890625 Factor a perfect square on the left side: (t + -2.125)(t + -2.125) = 0.890625 Calculate the square root of the right side: 0.943729304 Break this problem into two subproblems by setting (t + -2.125) equal to 0.943729304 and -0.943729304.Subproblem 1
t + -2.125 = 0.943729304 Simplifying t + -2.125 = 0.943729304 Reorder the terms: -2.125 + t = 0.943729304 Solving -2.125 + t = 0.943729304 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + t = 0.943729304 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + t = 0.943729304 + 2.125 t = 0.943729304 + 2.125 Combine like terms: 0.943729304 + 2.125 = 3.068729304 t = 3.068729304 Simplifying t = 3.068729304Subproblem 2
t + -2.125 = -0.943729304 Simplifying t + -2.125 = -0.943729304 Reorder the terms: -2.125 + t = -0.943729304 Solving -2.125 + t = -0.943729304 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.125' to each side of the equation. -2.125 + 2.125 + t = -0.943729304 + 2.125 Combine like terms: -2.125 + 2.125 = 0.000 0.000 + t = -0.943729304 + 2.125 t = -0.943729304 + 2.125 Combine like terms: -0.943729304 + 2.125 = 1.181270696 t = 1.181270696 Simplifying t = 1.181270696Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.068729304, 1.181270696}Solution
t = {3.068729304, 1.181270696}
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