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Simplifying 0 = 7(-2 + T2) + -15T 0 = (-2 * 7 + T2 * 7) + -15T 0 = (-14 + 7T2) + -15T Reorder the terms: 0 = -14 + -15T + 7T2 Solving 0 = -14 + -15T + 7T2 Solving for variable 'T'. Combine like terms: 0 + 14 = 14 14 + 15T + -7T2 = -14 + -15T + 7T2 + 14 + 15T + -7T2 Reorder the terms: 14 + 15T + -7T2 = -14 + 14 + -15T + 15T + 7T2 + -7T2 Combine like terms: -14 + 14 = 0 14 + 15T + -7T2 = 0 + -15T + 15T + 7T2 + -7T2 14 + 15T + -7T2 = -15T + 15T + 7T2 + -7T2 Combine like terms: -15T + 15T = 0 14 + 15T + -7T2 = 0 + 7T2 + -7T2 14 + 15T + -7T2 = 7T2 + -7T2 Combine like terms: 7T2 + -7T2 = 0 14 + 15T + -7T2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -2 + -2.142857143T + T2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -2.142857143T + 2 + T2 = 0 + 2 Reorder the terms: -2 + 2 + -2.142857143T + T2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -2.142857143T + T2 = 0 + 2 -2.142857143T + T2 = 0 + 2 Combine like terms: 0 + 2 = 2 -2.142857143T + T2 = 2 The T term is -2.142857143T. Take half its coefficient (-1.071428572). Square it (1.147959185) and add it to both sides. Add '1.147959185' to each side of the equation. -2.142857143T + 1.147959185 + T2 = 2 + 1.147959185 Reorder the terms: 1.147959185 + -2.142857143T + T2 = 2 + 1.147959185 Combine like terms: 2 + 1.147959185 = 3.147959185 1.147959185 + -2.142857143T + T2 = 3.147959185 Factor a perfect square on the left side: (T + -1.071428572)(T + -1.071428572) = 3.147959185 Calculate the square root of the right side: 1.774248907 Break this problem into two subproblems by setting (T + -1.071428572) equal to 1.774248907 and -1.774248907.Subproblem 1
T + -1.071428572 = 1.774248907 Simplifying T + -1.071428572 = 1.774248907 Reorder the terms: -1.071428572 + T = 1.774248907 Solving -1.071428572 + T = 1.774248907 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '1.071428572' to each side of the equation. -1.071428572 + 1.071428572 + T = 1.774248907 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + T = 1.774248907 + 1.071428572 T = 1.774248907 + 1.071428572 Combine like terms: 1.774248907 + 1.071428572 = 2.845677479 T = 2.845677479 Simplifying T = 2.845677479Subproblem 2
T + -1.071428572 = -1.774248907 Simplifying T + -1.071428572 = -1.774248907 Reorder the terms: -1.071428572 + T = -1.774248907 Solving -1.071428572 + T = -1.774248907 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '1.071428572' to each side of the equation. -1.071428572 + 1.071428572 + T = -1.774248907 + 1.071428572 Combine like terms: -1.071428572 + 1.071428572 = 0.000000000 0.000000000 + T = -1.774248907 + 1.071428572 T = -1.774248907 + 1.071428572 Combine like terms: -1.774248907 + 1.071428572 = -0.702820335 T = -0.702820335 Simplifying T = -0.702820335Solution
The solution to the problem is based on the solutions from the subproblems. T = {2.845677479, -0.702820335}
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