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Simplifying -5T2 + 16T + 30 = 0 Reorder the terms: 30 + 16T + -5T2 = 0 Solving 30 + 16T + -5T2 = 0 Solving for variable 'T'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -6 + -3.2T + T2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -3.2T + 6 + T2 = 0 + 6 Reorder the terms: -6 + 6 + -3.2T + T2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -3.2T + T2 = 0 + 6 -3.2T + T2 = 0 + 6 Combine like terms: 0 + 6 = 6 -3.2T + T2 = 6 The T term is -3.2T. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2T + 2.56 + T2 = 6 + 2.56 Reorder the terms: 2.56 + -3.2T + T2 = 6 + 2.56 Combine like terms: 6 + 2.56 = 8.56 2.56 + -3.2T + T2 = 8.56 Factor a perfect square on the left side: (T + -1.6)(T + -1.6) = 8.56 Calculate the square root of the right side: 2.925747768 Break this problem into two subproblems by setting (T + -1.6) equal to 2.925747768 and -2.925747768.Subproblem 1
T + -1.6 = 2.925747768 Simplifying T + -1.6 = 2.925747768 Reorder the terms: -1.6 + T = 2.925747768 Solving -1.6 + T = 2.925747768 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + T = 2.925747768 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + T = 2.925747768 + 1.6 T = 2.925747768 + 1.6 Combine like terms: 2.925747768 + 1.6 = 4.525747768 T = 4.525747768 Simplifying T = 4.525747768Subproblem 2
T + -1.6 = -2.925747768 Simplifying T + -1.6 = -2.925747768 Reorder the terms: -1.6 + T = -2.925747768 Solving -1.6 + T = -2.925747768 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + T = -2.925747768 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + T = -2.925747768 + 1.6 T = -2.925747768 + 1.6 Combine like terms: -2.925747768 + 1.6 = -1.325747768 T = -1.325747768 Simplifying T = -1.325747768Solution
The solution to the problem is based on the solutions from the subproblems. T = {4.525747768, -1.325747768}
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