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Simplifying 0 = -16t2 + 30t + 10 Reorder the terms: 0 = 10 + 30t + -16t2 Solving 0 = 10 + 30t + -16t2 Solving for variable 't'. Combine like terms: 0 + -10 = -10 -10 + -30t + 16t2 = 10 + 30t + -16t2 + -10 + -30t + 16t2 Reorder the terms: -10 + -30t + 16t2 = 10 + -10 + 30t + -30t + -16t2 + 16t2 Combine like terms: 10 + -10 = 0 -10 + -30t + 16t2 = 0 + 30t + -30t + -16t2 + 16t2 -10 + -30t + 16t2 = 30t + -30t + -16t2 + 16t2 Combine like terms: 30t + -30t = 0 -10 + -30t + 16t2 = 0 + -16t2 + 16t2 -10 + -30t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -10 + -30t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -15t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -15t + 8t2)' equal to zero and attempt to solve: Simplifying -5 + -15t + 8t2 = 0 Solving -5 + -15t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + -1.875t + t2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -1.875t + 0.625 + t2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -1.875t + t2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -1.875t + t2 = 0 + 0.625 -1.875t + t2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -1.875t + t2 = 0.625 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 = 0.625 + 0.87890625 Reorder the terms: 0.87890625 + -1.875t + t2 = 0.625 + 0.87890625 Combine like terms: 0.625 + 0.87890625 = 1.50390625 0.87890625 + -1.875t + t2 = 1.50390625 Factor a perfect square on the left side: (t + -0.9375)(t + -0.9375) = 1.50390625 Calculate the square root of the right side: 1.226338554 Break this problem into two subproblems by setting (t + -0.9375) equal to 1.226338554 and -1.226338554.Subproblem 1
t + -0.9375 = 1.226338554 Simplifying t + -0.9375 = 1.226338554 Reorder the terms: -0.9375 + t = 1.226338554 Solving -0.9375 + t = 1.226338554 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 = 1.226338554 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + t = 1.226338554 + 0.9375 t = 1.226338554 + 0.9375 Combine like terms: 1.226338554 + 0.9375 = 2.163838554 t = 2.163838554 Simplifying t = 2.163838554Subproblem 2
t + -0.9375 = -1.226338554 Simplifying t + -0.9375 = -1.226338554 Reorder the terms: -0.9375 + t = -1.226338554 Solving -0.9375 + t = -1.226338554 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 = -1.226338554 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + t = -1.226338554 + 0.9375 t = -1.226338554 + 0.9375 Combine like terms: -1.226338554 + 0.9375 = -0.288838554 t = -0.288838554 Simplifying t = -0.288838554Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.163838554, -0.288838554}Solution
t = {2.163838554, -0.288838554}
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