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Simplifying 15 = 139 + -15t + -16t2 Solving 15 = 139 + -15t + -16t2 Solving for variable 't'. Combine like terms: 15 + -139 = -124 -124 + 15t + 16t2 = 139 + -15t + -16t2 + -139 + 15t + 16t2 Reorder the terms: -124 + 15t + 16t2 = 139 + -139 + -15t + 15t + -16t2 + 16t2 Combine like terms: 139 + -139 = 0 -124 + 15t + 16t2 = 0 + -15t + 15t + -16t2 + 16t2 -124 + 15t + 16t2 = -15t + 15t + -16t2 + 16t2 Combine like terms: -15t + 15t = 0 -124 + 15t + 16t2 = 0 + -16t2 + 16t2 -124 + 15t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -124 + 15t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -7.75 + 0.9375t + t2 = 0 Move the constant term to the right: Add '7.75' to each side of the equation. -7.75 + 0.9375t + 7.75 + t2 = 0 + 7.75 Reorder the terms: -7.75 + 7.75 + 0.9375t + t2 = 0 + 7.75 Combine like terms: -7.75 + 7.75 = 0.00 0.00 + 0.9375t + t2 = 0 + 7.75 0.9375t + t2 = 0 + 7.75 Combine like terms: 0 + 7.75 = 7.75 0.9375t + t2 = 7.75 The t term is 0.9375t. Take half its coefficient (0.46875). Square it (0.2197265625) and add it to both sides. Add '0.2197265625' to each side of the equation. 0.9375t + 0.2197265625 + t2 = 7.75 + 0.2197265625 Reorder the terms: 0.2197265625 + 0.9375t + t2 = 7.75 + 0.2197265625 Combine like terms: 7.75 + 0.2197265625 = 7.9697265625 0.2197265625 + 0.9375t + t2 = 7.9697265625 Factor a perfect square on the left side: (t + 0.46875)(t + 0.46875) = 7.9697265625 Calculate the square root of the right side: 2.823070414 Break this problem into two subproblems by setting (t + 0.46875) equal to 2.823070414 and -2.823070414.Subproblem 1
t + 0.46875 = 2.823070414 Simplifying t + 0.46875 = 2.823070414 Reorder the terms: 0.46875 + t = 2.823070414 Solving 0.46875 + t = 2.823070414 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.46875' to each side of the equation. 0.46875 + -0.46875 + t = 2.823070414 + -0.46875 Combine like terms: 0.46875 + -0.46875 = 0.00000 0.00000 + t = 2.823070414 + -0.46875 t = 2.823070414 + -0.46875 Combine like terms: 2.823070414 + -0.46875 = 2.354320414 t = 2.354320414 Simplifying t = 2.354320414Subproblem 2
t + 0.46875 = -2.823070414 Simplifying t + 0.46875 = -2.823070414 Reorder the terms: 0.46875 + t = -2.823070414 Solving 0.46875 + t = -2.823070414 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.46875' to each side of the equation. 0.46875 + -0.46875 + t = -2.823070414 + -0.46875 Combine like terms: 0.46875 + -0.46875 = 0.00000 0.00000 + t = -2.823070414 + -0.46875 t = -2.823070414 + -0.46875 Combine like terms: -2.823070414 + -0.46875 = -3.291820414 t = -3.291820414 Simplifying t = -3.291820414Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.354320414, -3.291820414}
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