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Simplifying 20 = -16t2 + 100t + 50 Reorder the terms: 20 = 50 + 100t + -16t2 Solving 20 = 50 + 100t + -16t2 Solving for variable 't'. Combine like terms: 20 + -50 = -30 -30 + -100t + 16t2 = 50 + 100t + -16t2 + -50 + -100t + 16t2 Reorder the terms: -30 + -100t + 16t2 = 50 + -50 + 100t + -100t + -16t2 + 16t2 Combine like terms: 50 + -50 = 0 -30 + -100t + 16t2 = 0 + 100t + -100t + -16t2 + 16t2 -30 + -100t + 16t2 = 100t + -100t + -16t2 + 16t2 Combine like terms: 100t + -100t = 0 -30 + -100t + 16t2 = 0 + -16t2 + 16t2 -30 + -100t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -30 + -100t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + -50t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + -50t + 8t2)' equal to zero and attempt to solve: Simplifying -15 + -50t + 8t2 = 0 Solving -15 + -50t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.875 + -6.25t + t2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + -6.25t + 1.875 + t2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + -6.25t + t2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + -6.25t + t2 = 0 + 1.875 -6.25t + t2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 -6.25t + t2 = 1.875 The t term is -6.25t. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25t + 9.765625 + t2 = 1.875 + 9.765625 Reorder the terms: 9.765625 + -6.25t + t2 = 1.875 + 9.765625 Combine like terms: 1.875 + 9.765625 = 11.640625 9.765625 + -6.25t + t2 = 11.640625 Factor a perfect square on the left side: (t + -3.125)(t + -3.125) = 11.640625 Calculate the square root of the right side: 3.411836016 Break this problem into two subproblems by setting (t + -3.125) equal to 3.411836016 and -3.411836016.Subproblem 1
t + -3.125 = 3.411836016 Simplifying t + -3.125 = 3.411836016 Reorder the terms: -3.125 + t = 3.411836016 Solving -3.125 + t = 3.411836016 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + t = 3.411836016 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + t = 3.411836016 + 3.125 t = 3.411836016 + 3.125 Combine like terms: 3.411836016 + 3.125 = 6.536836016 t = 6.536836016 Simplifying t = 6.536836016Subproblem 2
t + -3.125 = -3.411836016 Simplifying t + -3.125 = -3.411836016 Reorder the terms: -3.125 + t = -3.411836016 Solving -3.125 + t = -3.411836016 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + t = -3.411836016 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + t = -3.411836016 + 3.125 t = -3.411836016 + 3.125 Combine like terms: -3.411836016 + 3.125 = -0.286836016 t = -0.286836016 Simplifying t = -0.286836016Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.536836016, -0.286836016}Solution
t = {6.536836016, -0.286836016}
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