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Simplifying 0 = -16T2 + 80T + 100 Reorder the terms: 0 = 100 + 80T + -16T2 Solving 0 = 100 + 80T + -16T2 Solving for variable 'T'. Combine like terms: 0 + -100 = -100 -100 + -80T + 16T2 = 100 + 80T + -16T2 + -100 + -80T + 16T2 Reorder the terms: -100 + -80T + 16T2 = 100 + -100 + 80T + -80T + -16T2 + 16T2 Combine like terms: 100 + -100 = 0 -100 + -80T + 16T2 = 0 + 80T + -80T + -16T2 + 16T2 -100 + -80T + 16T2 = 80T + -80T + -16T2 + 16T2 Combine like terms: 80T + -80T = 0 -100 + -80T + 16T2 = 0 + -16T2 + 16T2 -100 + -80T + 16T2 = -16T2 + 16T2 Combine like terms: -16T2 + 16T2 = 0 -100 + -80T + 16T2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-25 + -20T + 4T2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-25 + -20T + 4T2)' equal to zero and attempt to solve: Simplifying -25 + -20T + 4T2 = 0 Solving -25 + -20T + 4T2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.25 + -5T + T2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -5T + 6.25 + T2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -5T + T2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -5T + T2 = 0 + 6.25 -5T + T2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -5T + T2 = 6.25 The T term is -5T. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5T + 6.25 + T2 = 6.25 + 6.25 Reorder the terms: 6.25 + -5T + T2 = 6.25 + 6.25 Combine like terms: 6.25 + 6.25 = 12.5 6.25 + -5T + T2 = 12.5 Factor a perfect square on the left side: (T + -2.5)(T + -2.5) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (T + -2.5) equal to 3.535533906 and -3.535533906.Subproblem 1
T + -2.5 = 3.535533906 Simplifying T + -2.5 = 3.535533906 Reorder the terms: -2.5 + T = 3.535533906 Solving -2.5 + T = 3.535533906 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + T = 3.535533906 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + T = 3.535533906 + 2.5 T = 3.535533906 + 2.5 Combine like terms: 3.535533906 + 2.5 = 6.035533906 T = 6.035533906 Simplifying T = 6.035533906Subproblem 2
T + -2.5 = -3.535533906 Simplifying T + -2.5 = -3.535533906 Reorder the terms: -2.5 + T = -3.535533906 Solving -2.5 + T = -3.535533906 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + T = -3.535533906 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + T = -3.535533906 + 2.5 T = -3.535533906 + 2.5 Combine like terms: -3.535533906 + 2.5 = -1.035533906 T = -1.035533906 Simplifying T = -1.035533906Solution
The solution to the problem is based on the solutions from the subproblems. T = {6.035533906, -1.035533906}Solution
T = {6.035533906, -1.035533906}
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