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Simplifying 5 = 16t2 + 126t Reorder the terms: 5 = 126t + 16t2 Solving 5 = 126t + 16t2 Solving for variable 't'. Reorder the terms: 5 + -126t + -16t2 = 126t + -126t + 16t2 + -16t2 Combine like terms: 126t + -126t = 0 5 + -126t + -16t2 = 0 + 16t2 + -16t2 5 + -126t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 5 + -126t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.3125 + 7.875t + t2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + 7.875t + 0.3125 + t2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + 7.875t + t2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + 7.875t + t2 = 0 + 0.3125 7.875t + t2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 7.875t + t2 = 0.3125 The t term is 7.875t. Take half its coefficient (3.9375). Square it (15.50390625) and add it to both sides. Add '15.50390625' to each side of the equation. 7.875t + 15.50390625 + t2 = 0.3125 + 15.50390625 Reorder the terms: 15.50390625 + 7.875t + t2 = 0.3125 + 15.50390625 Combine like terms: 0.3125 + 15.50390625 = 15.81640625 15.50390625 + 7.875t + t2 = 15.81640625 Factor a perfect square on the left side: (t + 3.9375)(t + 3.9375) = 15.81640625 Calculate the square root of the right side: 3.976984567 Break this problem into two subproblems by setting (t + 3.9375) equal to 3.976984567 and -3.976984567.Subproblem 1
t + 3.9375 = 3.976984567 Simplifying t + 3.9375 = 3.976984567 Reorder the terms: 3.9375 + t = 3.976984567 Solving 3.9375 + t = 3.976984567 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.9375' to each side of the equation. 3.9375 + -3.9375 + t = 3.976984567 + -3.9375 Combine like terms: 3.9375 + -3.9375 = 0.0000 0.0000 + t = 3.976984567 + -3.9375 t = 3.976984567 + -3.9375 Combine like terms: 3.976984567 + -3.9375 = 0.039484567 t = 0.039484567 Simplifying t = 0.039484567Subproblem 2
t + 3.9375 = -3.976984567 Simplifying t + 3.9375 = -3.976984567 Reorder the terms: 3.9375 + t = -3.976984567 Solving 3.9375 + t = -3.976984567 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.9375' to each side of the equation. 3.9375 + -3.9375 + t = -3.976984567 + -3.9375 Combine like terms: 3.9375 + -3.9375 = 0.0000 0.0000 + t = -3.976984567 + -3.9375 t = -3.976984567 + -3.9375 Combine like terms: -3.976984567 + -3.9375 = -7.914484567 t = -7.914484567 Simplifying t = -7.914484567Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.039484567, -7.914484567}
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