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Simplifying 400 = -16t2 + 240t + 8 Reorder the terms: 400 = 8 + 240t + -16t2 Solving 400 = 8 + 240t + -16t2 Solving for variable 't'. Combine like terms: 400 + -8 = 392 392 + -240t + 16t2 = 8 + 240t + -16t2 + -8 + -240t + 16t2 Reorder the terms: 392 + -240t + 16t2 = 8 + -8 + 240t + -240t + -16t2 + 16t2 Combine like terms: 8 + -8 = 0 392 + -240t + 16t2 = 0 + 240t + -240t + -16t2 + 16t2 392 + -240t + 16t2 = 240t + -240t + -16t2 + 16t2 Combine like terms: 240t + -240t = 0 392 + -240t + 16t2 = 0 + -16t2 + 16t2 392 + -240t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 392 + -240t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(49 + -30t + 2t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(49 + -30t + 2t2)' equal to zero and attempt to solve: Simplifying 49 + -30t + 2t2 = 0 Solving 49 + -30t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 24.5 + -15t + t2 = 0 Move the constant term to the right: Add '-24.5' to each side of the equation. 24.5 + -15t + -24.5 + t2 = 0 + -24.5 Reorder the terms: 24.5 + -24.5 + -15t + t2 = 0 + -24.5 Combine like terms: 24.5 + -24.5 = 0.0 0.0 + -15t + t2 = 0 + -24.5 -15t + t2 = 0 + -24.5 Combine like terms: 0 + -24.5 = -24.5 -15t + t2 = -24.5 The t term is -15t. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15t + 56.25 + t2 = -24.5 + 56.25 Reorder the terms: 56.25 + -15t + t2 = -24.5 + 56.25 Combine like terms: -24.5 + 56.25 = 31.75 56.25 + -15t + t2 = 31.75 Factor a perfect square on the left side: (t + -7.5)(t + -7.5) = 31.75 Calculate the square root of the right side: 5.634713835 Break this problem into two subproblems by setting (t + -7.5) equal to 5.634713835 and -5.634713835.Subproblem 1
t + -7.5 = 5.634713835 Simplifying t + -7.5 = 5.634713835 Reorder the terms: -7.5 + t = 5.634713835 Solving -7.5 + t = 5.634713835 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + t = 5.634713835 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + t = 5.634713835 + 7.5 t = 5.634713835 + 7.5 Combine like terms: 5.634713835 + 7.5 = 13.134713835 t = 13.134713835 Simplifying t = 13.134713835Subproblem 2
t + -7.5 = -5.634713835 Simplifying t + -7.5 = -5.634713835 Reorder the terms: -7.5 + t = -5.634713835 Solving -7.5 + t = -5.634713835 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + t = -5.634713835 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + t = -5.634713835 + 7.5 t = -5.634713835 + 7.5 Combine like terms: -5.634713835 + 7.5 = 1.865286165 t = 1.865286165 Simplifying t = 1.865286165Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.134713835, 1.865286165}Solution
t = {13.134713835, 1.865286165}
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