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Simplifying -2t2 + 15t + -15 = 0 Reorder the terms: -15 + 15t + -2t2 = 0 Solving -15 + 15t + -2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 7.5 + -7.5t + t2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + -7.5t + -7.5 + t2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + -7.5t + t2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + -7.5t + t2 = 0 + -7.5 -7.5t + t2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 -7.5t + t2 = -7.5 The t term is -7.5t. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5t + 14.0625 + t2 = -7.5 + 14.0625 Reorder the terms: 14.0625 + -7.5t + t2 = -7.5 + 14.0625 Combine like terms: -7.5 + 14.0625 = 6.5625 14.0625 + -7.5t + t2 = 6.5625 Factor a perfect square on the left side: (t + -3.75)(t + -3.75) = 6.5625 Calculate the square root of the right side: 2.561737691 Break this problem into two subproblems by setting (t + -3.75) equal to 2.561737691 and -2.561737691.Subproblem 1
t + -3.75 = 2.561737691 Simplifying t + -3.75 = 2.561737691 Reorder the terms: -3.75 + t = 2.561737691 Solving -3.75 + t = 2.561737691 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + t = 2.561737691 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + t = 2.561737691 + 3.75 t = 2.561737691 + 3.75 Combine like terms: 2.561737691 + 3.75 = 6.311737691 t = 6.311737691 Simplifying t = 6.311737691Subproblem 2
t + -3.75 = -2.561737691 Simplifying t + -3.75 = -2.561737691 Reorder the terms: -3.75 + t = -2.561737691 Solving -3.75 + t = -2.561737691 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + t = -2.561737691 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + t = -2.561737691 + 3.75 t = -2.561737691 + 3.75 Combine like terms: -2.561737691 + 3.75 = 1.188262309 t = 1.188262309 Simplifying t = 1.188262309Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.311737691, 1.188262309}
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