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Simplifying T2 + 14T + -40 = 0 Reorder the terms: -40 + 14T + T2 = 0 Solving -40 + 14T + T2 = 0 Solving for variable 'T'. Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + 14T + 40 + T2 = 0 + 40 Reorder the terms: -40 + 40 + 14T + T2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 14T + T2 = 0 + 40 14T + T2 = 0 + 40 Combine like terms: 0 + 40 = 40 14T + T2 = 40 The T term is 14T. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14T + 49 + T2 = 40 + 49 Reorder the terms: 49 + 14T + T2 = 40 + 49 Combine like terms: 40 + 49 = 89 49 + 14T + T2 = 89 Factor a perfect square on the left side: (T + 7)(T + 7) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (T + 7) equal to 9.433981132 and -9.433981132.Subproblem 1
T + 7 = 9.433981132 Simplifying T + 7 = 9.433981132 Reorder the terms: 7 + T = 9.433981132 Solving 7 + T = 9.433981132 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + T = 9.433981132 + -7 Combine like terms: 7 + -7 = 0 0 + T = 9.433981132 + -7 T = 9.433981132 + -7 Combine like terms: 9.433981132 + -7 = 2.433981132 T = 2.433981132 Simplifying T = 2.433981132Subproblem 2
T + 7 = -9.433981132 Simplifying T + 7 = -9.433981132 Reorder the terms: 7 + T = -9.433981132 Solving 7 + T = -9.433981132 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + T = -9.433981132 + -7 Combine like terms: 7 + -7 = 0 0 + T = -9.433981132 + -7 T = -9.433981132 + -7 Combine like terms: -9.433981132 + -7 = -16.433981132 T = -16.433981132 Simplifying T = -16.433981132Solution
The solution to the problem is based on the solutions from the subproblems. T = {2.433981132, -16.433981132}
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