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Simplifying 1538 = -16T2 + 320T + 0 Reorder the terms: 1538 = 0 + 320T + -16T2 Remove the zero: 1538 = 320T + -16T2 Solving 1538 = 320T + -16T2 Solving for variable 'T'. Reorder the terms: 1538 + -320T + 16T2 = 320T + -320T + -16T2 + 16T2 Combine like terms: 320T + -320T = 0 1538 + -320T + 16T2 = 0 + -16T2 + 16T2 1538 + -320T + 16T2 = -16T2 + 16T2 Combine like terms: -16T2 + 16T2 = 0 1538 + -320T + 16T2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(769 + -160T + 8T2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(769 + -160T + 8T2)' equal to zero and attempt to solve: Simplifying 769 + -160T + 8T2 = 0 Solving 769 + -160T + 8T2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 96.125 + -20T + T2 = 0 Move the constant term to the right: Add '-96.125' to each side of the equation. 96.125 + -20T + -96.125 + T2 = 0 + -96.125 Reorder the terms: 96.125 + -96.125 + -20T + T2 = 0 + -96.125 Combine like terms: 96.125 + -96.125 = 0.000 0.000 + -20T + T2 = 0 + -96.125 -20T + T2 = 0 + -96.125 Combine like terms: 0 + -96.125 = -96.125 -20T + T2 = -96.125 The T term is -20T. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20T + 100 + T2 = -96.125 + 100 Reorder the terms: 100 + -20T + T2 = -96.125 + 100 Combine like terms: -96.125 + 100 = 3.875 100 + -20T + T2 = 3.875 Factor a perfect square on the left side: (T + -10)(T + -10) = 3.875 Calculate the square root of the right side: 1.968501969 Break this problem into two subproblems by setting (T + -10) equal to 1.968501969 and -1.968501969.Subproblem 1
T + -10 = 1.968501969 Simplifying T + -10 = 1.968501969 Reorder the terms: -10 + T = 1.968501969 Solving -10 + T = 1.968501969 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + T = 1.968501969 + 10 Combine like terms: -10 + 10 = 0 0 + T = 1.968501969 + 10 T = 1.968501969 + 10 Combine like terms: 1.968501969 + 10 = 11.968501969 T = 11.968501969 Simplifying T = 11.968501969Subproblem 2
T + -10 = -1.968501969 Simplifying T + -10 = -1.968501969 Reorder the terms: -10 + T = -1.968501969 Solving -10 + T = -1.968501969 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + T = -1.968501969 + 10 Combine like terms: -10 + 10 = 0 0 + T = -1.968501969 + 10 T = -1.968501969 + 10 Combine like terms: -1.968501969 + 10 = 8.031498031 T = 8.031498031 Simplifying T = 8.031498031Solution
The solution to the problem is based on the solutions from the subproblems. T = {11.968501969, 8.031498031}Solution
T = {11.968501969, 8.031498031}
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