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Simplifying -16t2 + -30t + 280 = 0 Reorder the terms: 280 + -30t + -16t2 = 0 Solving 280 + -30t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(140 + -15t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(140 + -15t + -8t2)' equal to zero and attempt to solve: Simplifying 140 + -15t + -8t2 = 0 Solving 140 + -15t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -17.5 + 1.875t + t2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + 1.875t + 17.5 + t2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + 1.875t + t2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + 1.875t + t2 = 0 + 17.5 1.875t + t2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 1.875t + t2 = 17.5 The t term is 1.875t. Take half its coefficient (0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. 1.875t + 0.87890625 + t2 = 17.5 + 0.87890625 Reorder the terms: 0.87890625 + 1.875t + t2 = 17.5 + 0.87890625 Combine like terms: 17.5 + 0.87890625 = 18.37890625 0.87890625 + 1.875t + t2 = 18.37890625 Factor a perfect square on the left side: (t + 0.9375)(t + 0.9375) = 18.37890625 Calculate the square root of the right side: 4.28706266 Break this problem into two subproblems by setting (t + 0.9375) equal to 4.28706266 and -4.28706266.Subproblem 1
t + 0.9375 = 4.28706266 Simplifying t + 0.9375 = 4.28706266 Reorder the terms: 0.9375 + t = 4.28706266 Solving 0.9375 + t = 4.28706266 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + t = 4.28706266 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + t = 4.28706266 + -0.9375 t = 4.28706266 + -0.9375 Combine like terms: 4.28706266 + -0.9375 = 3.34956266 t = 3.34956266 Simplifying t = 3.34956266Subproblem 2
t + 0.9375 = -4.28706266 Simplifying t + 0.9375 = -4.28706266 Reorder the terms: 0.9375 + t = -4.28706266 Solving 0.9375 + t = -4.28706266 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + t = -4.28706266 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + t = -4.28706266 + -0.9375 t = -4.28706266 + -0.9375 Combine like terms: -4.28706266 + -0.9375 = -5.22456266 t = -5.22456266 Simplifying t = -5.22456266Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.34956266, -5.22456266}Solution
t = {3.34956266, -5.22456266}
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