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Simplifying 0 = 16t2 + 75t + 4 Reorder the terms: 0 = 4 + 75t + 16t2 Solving 0 = 4 + 75t + 16t2 Solving for variable 't'. Combine like terms: 0 + -4 = -4 -4 + -75t + -16t2 = 4 + 75t + 16t2 + -4 + -75t + -16t2 Reorder the terms: -4 + -75t + -16t2 = 4 + -4 + 75t + -75t + 16t2 + -16t2 Combine like terms: 4 + -4 = 0 -4 + -75t + -16t2 = 0 + 75t + -75t + 16t2 + -16t2 -4 + -75t + -16t2 = 75t + -75t + 16t2 + -16t2 Combine like terms: 75t + -75t = 0 -4 + -75t + -16t2 = 0 + 16t2 + -16t2 -4 + -75t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -4 + -75t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 75t + 16t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 75t + 16t2)' equal to zero and attempt to solve: Simplifying 4 + 75t + 16t2 = 0 Solving 4 + 75t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.25 + 4.6875t + t2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 4.6875t + -0.25 + t2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 4.6875t + t2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 4.6875t + t2 = 0 + -0.25 4.6875t + t2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 4.6875t + t2 = -0.25 The t term is 4.6875t. Take half its coefficient (2.34375). Square it (5.493164063) and add it to both sides. Add '5.493164063' to each side of the equation. 4.6875t + 5.493164063 + t2 = -0.25 + 5.493164063 Reorder the terms: 5.493164063 + 4.6875t + t2 = -0.25 + 5.493164063 Combine like terms: -0.25 + 5.493164063 = 5.243164063 5.493164063 + 4.6875t + t2 = 5.243164063 Factor a perfect square on the left side: (t + 2.34375)(t + 2.34375) = 5.243164063 Calculate the square root of the right side: 2.289795638 Break this problem into two subproblems by setting (t + 2.34375) equal to 2.289795638 and -2.289795638.Subproblem 1
t + 2.34375 = 2.289795638 Simplifying t + 2.34375 = 2.289795638 Reorder the terms: 2.34375 + t = 2.289795638 Solving 2.34375 + t = 2.289795638 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.34375' to each side of the equation. 2.34375 + -2.34375 + t = 2.289795638 + -2.34375 Combine like terms: 2.34375 + -2.34375 = 0.00000 0.00000 + t = 2.289795638 + -2.34375 t = 2.289795638 + -2.34375 Combine like terms: 2.289795638 + -2.34375 = -0.053954362 t = -0.053954362 Simplifying t = -0.053954362Subproblem 2
t + 2.34375 = -2.289795638 Simplifying t + 2.34375 = -2.289795638 Reorder the terms: 2.34375 + t = -2.289795638 Solving 2.34375 + t = -2.289795638 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.34375' to each side of the equation. 2.34375 + -2.34375 + t = -2.289795638 + -2.34375 Combine like terms: 2.34375 + -2.34375 = 0.00000 0.00000 + t = -2.289795638 + -2.34375 t = -2.289795638 + -2.34375 Combine like terms: -2.289795638 + -2.34375 = -4.633545638 t = -4.633545638 Simplifying t = -4.633545638Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.053954362, -4.633545638}Solution
t = {-0.053954362, -4.633545638}
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