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Simplifying t = -16t2 + 63t + 4 Reorder the terms: t = 4 + 63t + -16t2 Solving t = 4 + 63t + -16t2 Solving for variable 't'. Reorder the terms: -4 + t + -63t + 16t2 = 4 + 63t + -16t2 + -4 + -63t + 16t2 Combine like terms: t + -63t = -62t -4 + -62t + 16t2 = 4 + 63t + -16t2 + -4 + -63t + 16t2 Reorder the terms: -4 + -62t + 16t2 = 4 + -4 + 63t + -63t + -16t2 + 16t2 Combine like terms: 4 + -4 = 0 -4 + -62t + 16t2 = 0 + 63t + -63t + -16t2 + 16t2 -4 + -62t + 16t2 = 63t + -63t + -16t2 + 16t2 Combine like terms: 63t + -63t = 0 -4 + -62t + 16t2 = 0 + -16t2 + 16t2 -4 + -62t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -4 + -62t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -31t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + -31t + 8t2)' equal to zero and attempt to solve: Simplifying -2 + -31t + 8t2 = 0 Solving -2 + -31t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.25 + -3.875t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -3.875t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -3.875t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -3.875t + t2 = 0 + 0.25 -3.875t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -3.875t + t2 = 0.25 The t term is -3.875t. Take half its coefficient (-1.9375). Square it (3.75390625) and add it to both sides. Add '3.75390625' to each side of the equation. -3.875t + 3.75390625 + t2 = 0.25 + 3.75390625 Reorder the terms: 3.75390625 + -3.875t + t2 = 0.25 + 3.75390625 Combine like terms: 0.25 + 3.75390625 = 4.00390625 3.75390625 + -3.875t + t2 = 4.00390625 Factor a perfect square on the left side: (t + -1.9375)(t + -1.9375) = 4.00390625 Calculate the square root of the right side: 2.000976324 Break this problem into two subproblems by setting (t + -1.9375) equal to 2.000976324 and -2.000976324.Subproblem 1
t + -1.9375 = 2.000976324 Simplifying t + -1.9375 = 2.000976324 Reorder the terms: -1.9375 + t = 2.000976324 Solving -1.9375 + t = 2.000976324 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.9375' to each side of the equation. -1.9375 + 1.9375 + t = 2.000976324 + 1.9375 Combine like terms: -1.9375 + 1.9375 = 0.0000 0.0000 + t = 2.000976324 + 1.9375 t = 2.000976324 + 1.9375 Combine like terms: 2.000976324 + 1.9375 = 3.938476324 t = 3.938476324 Simplifying t = 3.938476324Subproblem 2
t + -1.9375 = -2.000976324 Simplifying t + -1.9375 = -2.000976324 Reorder the terms: -1.9375 + t = -2.000976324 Solving -1.9375 + t = -2.000976324 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.9375' to each side of the equation. -1.9375 + 1.9375 + t = -2.000976324 + 1.9375 Combine like terms: -1.9375 + 1.9375 = 0.0000 0.0000 + t = -2.000976324 + 1.9375 t = -2.000976324 + 1.9375 Combine like terms: -2.000976324 + 1.9375 = -0.063476324 t = -0.063476324 Simplifying t = -0.063476324Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.938476324, -0.063476324}Solution
t = {3.938476324, -0.063476324}
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