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Simplifying 25 = 5 + 37T + 16T2 Solving 25 = 5 + 37T + 16T2 Solving for variable 'T'. Combine like terms: 25 + -5 = 20 20 + -37T + -16T2 = 5 + 37T + 16T2 + -5 + -37T + -16T2 Reorder the terms: 20 + -37T + -16T2 = 5 + -5 + 37T + -37T + 16T2 + -16T2 Combine like terms: 5 + -5 = 0 20 + -37T + -16T2 = 0 + 37T + -37T + 16T2 + -16T2 20 + -37T + -16T2 = 37T + -37T + 16T2 + -16T2 Combine like terms: 37T + -37T = 0 20 + -37T + -16T2 = 0 + 16T2 + -16T2 20 + -37T + -16T2 = 16T2 + -16T2 Combine like terms: 16T2 + -16T2 = 0 20 + -37T + -16T2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -1.25 + 2.3125T + T2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 2.3125T + 1.25 + T2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 2.3125T + T2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 2.3125T + T2 = 0 + 1.25 2.3125T + T2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 2.3125T + T2 = 1.25 The T term is 2.3125T. Take half its coefficient (1.15625). Square it (1.336914063) and add it to both sides. Add '1.336914063' to each side of the equation. 2.3125T + 1.336914063 + T2 = 1.25 + 1.336914063 Reorder the terms: 1.336914063 + 2.3125T + T2 = 1.25 + 1.336914063 Combine like terms: 1.25 + 1.336914063 = 2.586914063 1.336914063 + 2.3125T + T2 = 2.586914063 Factor a perfect square on the left side: (T + 1.15625)(T + 1.15625) = 2.586914063 Calculate the square root of the right side: 1.608388654 Break this problem into two subproblems by setting (T + 1.15625) equal to 1.608388654 and -1.608388654.Subproblem 1
T + 1.15625 = 1.608388654 Simplifying T + 1.15625 = 1.608388654 Reorder the terms: 1.15625 + T = 1.608388654 Solving 1.15625 + T = 1.608388654 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '-1.15625' to each side of the equation. 1.15625 + -1.15625 + T = 1.608388654 + -1.15625 Combine like terms: 1.15625 + -1.15625 = 0.00000 0.00000 + T = 1.608388654 + -1.15625 T = 1.608388654 + -1.15625 Combine like terms: 1.608388654 + -1.15625 = 0.452138654 T = 0.452138654 Simplifying T = 0.452138654Subproblem 2
T + 1.15625 = -1.608388654 Simplifying T + 1.15625 = -1.608388654 Reorder the terms: 1.15625 + T = -1.608388654 Solving 1.15625 + T = -1.608388654 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '-1.15625' to each side of the equation. 1.15625 + -1.15625 + T = -1.608388654 + -1.15625 Combine like terms: 1.15625 + -1.15625 = 0.00000 0.00000 + T = -1.608388654 + -1.15625 T = -1.608388654 + -1.15625 Combine like terms: -1.608388654 + -1.15625 = -2.764638654 T = -2.764638654 Simplifying T = -2.764638654Solution
The solution to the problem is based on the solutions from the subproblems. T = {0.452138654, -2.764638654}
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