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Simplifying 300 = -16t2 + 112t + 128 Reorder the terms: 300 = 128 + 112t + -16t2 Solving 300 = 128 + 112t + -16t2 Solving for variable 't'. Combine like terms: 300 + -128 = 172 172 + -112t + 16t2 = 128 + 112t + -16t2 + -128 + -112t + 16t2 Reorder the terms: 172 + -112t + 16t2 = 128 + -128 + 112t + -112t + -16t2 + 16t2 Combine like terms: 128 + -128 = 0 172 + -112t + 16t2 = 0 + 112t + -112t + -16t2 + 16t2 172 + -112t + 16t2 = 112t + -112t + -16t2 + 16t2 Combine like terms: 112t + -112t = 0 172 + -112t + 16t2 = 0 + -16t2 + 16t2 172 + -112t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 172 + -112t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(43 + -28t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(43 + -28t + 4t2)' equal to zero and attempt to solve: Simplifying 43 + -28t + 4t2 = 0 Solving 43 + -28t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 10.75 + -7t + t2 = 0 Move the constant term to the right: Add '-10.75' to each side of the equation. 10.75 + -7t + -10.75 + t2 = 0 + -10.75 Reorder the terms: 10.75 + -10.75 + -7t + t2 = 0 + -10.75 Combine like terms: 10.75 + -10.75 = 0.00 0.00 + -7t + t2 = 0 + -10.75 -7t + t2 = 0 + -10.75 Combine like terms: 0 + -10.75 = -10.75 -7t + t2 = -10.75 The t term is -7t. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7t + 12.25 + t2 = -10.75 + 12.25 Reorder the terms: 12.25 + -7t + t2 = -10.75 + 12.25 Combine like terms: -10.75 + 12.25 = 1.5 12.25 + -7t + t2 = 1.5 Factor a perfect square on the left side: (t + -3.5)(t + -3.5) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (t + -3.5) equal to 1.224744871 and -1.224744871.Subproblem 1
t + -3.5 = 1.224744871 Simplifying t + -3.5 = 1.224744871 Reorder the terms: -3.5 + t = 1.224744871 Solving -3.5 + t = 1.224744871 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = 1.224744871 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = 1.224744871 + 3.5 t = 1.224744871 + 3.5 Combine like terms: 1.224744871 + 3.5 = 4.724744871 t = 4.724744871 Simplifying t = 4.724744871Subproblem 2
t + -3.5 = -1.224744871 Simplifying t + -3.5 = -1.224744871 Reorder the terms: -3.5 + t = -1.224744871 Solving -3.5 + t = -1.224744871 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = -1.224744871 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = -1.224744871 + 3.5 t = -1.224744871 + 3.5 Combine like terms: -1.224744871 + 3.5 = 2.275255129 t = 2.275255129 Simplifying t = 2.275255129Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.724744871, 2.275255129}Solution
t = {4.724744871, 2.275255129}
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