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Simplifying -16T2 + 50T + -24 = 0 Reorder the terms: -24 + 50T + -16T2 = 0 Solving -24 + 50T + -16T2 = 0 Solving for variable 'T'. Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 25T + -8T2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + 25T + -8T2)' equal to zero and attempt to solve: Simplifying -12 + 25T + -8T2 = 0 Solving -12 + 25T + -8T2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 1.5 + -3.125T + T2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -3.125T + -1.5 + T2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -3.125T + T2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -3.125T + T2 = 0 + -1.5 -3.125T + T2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -3.125T + T2 = -1.5 The T term is -3.125T. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125T + 2.44140625 + T2 = -1.5 + 2.44140625 Reorder the terms: 2.44140625 + -3.125T + T2 = -1.5 + 2.44140625 Combine like terms: -1.5 + 2.44140625 = 0.94140625 2.44140625 + -3.125T + T2 = 0.94140625 Factor a perfect square on the left side: (T + -1.5625)(T + -1.5625) = 0.94140625 Calculate the square root of the right side: 0.970260919 Break this problem into two subproblems by setting (T + -1.5625) equal to 0.970260919 and -0.970260919.Subproblem 1
T + -1.5625 = 0.970260919 Simplifying T + -1.5625 = 0.970260919 Reorder the terms: -1.5625 + T = 0.970260919 Solving -1.5625 + T = 0.970260919 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + T = 0.970260919 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + T = 0.970260919 + 1.5625 T = 0.970260919 + 1.5625 Combine like terms: 0.970260919 + 1.5625 = 2.532760919 T = 2.532760919 Simplifying T = 2.532760919Subproblem 2
T + -1.5625 = -0.970260919 Simplifying T + -1.5625 = -0.970260919 Reorder the terms: -1.5625 + T = -0.970260919 Solving -1.5625 + T = -0.970260919 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + T = -0.970260919 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + T = -0.970260919 + 1.5625 T = -0.970260919 + 1.5625 Combine like terms: -0.970260919 + 1.5625 = 0.592239081 T = 0.592239081 Simplifying T = 0.592239081Solution
The solution to the problem is based on the solutions from the subproblems. T = {2.532760919, 0.592239081}Solution
T = {2.532760919, 0.592239081}
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