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Simplifying 0 = -4T2 + 3T + 375 Reorder the terms: 0 = 375 + 3T + -4T2 Solving 0 = 375 + 3T + -4T2 Solving for variable 'T'. Combine like terms: 0 + -375 = -375 -375 + -3T + 4T2 = 375 + 3T + -4T2 + -375 + -3T + 4T2 Reorder the terms: -375 + -3T + 4T2 = 375 + -375 + 3T + -3T + -4T2 + 4T2 Combine like terms: 375 + -375 = 0 -375 + -3T + 4T2 = 0 + 3T + -3T + -4T2 + 4T2 -375 + -3T + 4T2 = 3T + -3T + -4T2 + 4T2 Combine like terms: 3T + -3T = 0 -375 + -3T + 4T2 = 0 + -4T2 + 4T2 -375 + -3T + 4T2 = -4T2 + 4T2 Combine like terms: -4T2 + 4T2 = 0 -375 + -3T + 4T2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -93.75 + -0.75T + T2 = 0 Move the constant term to the right: Add '93.75' to each side of the equation. -93.75 + -0.75T + 93.75 + T2 = 0 + 93.75 Reorder the terms: -93.75 + 93.75 + -0.75T + T2 = 0 + 93.75 Combine like terms: -93.75 + 93.75 = 0.00 0.00 + -0.75T + T2 = 0 + 93.75 -0.75T + T2 = 0 + 93.75 Combine like terms: 0 + 93.75 = 93.75 -0.75T + T2 = 93.75 The T term is -0.75T. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75T + 0.140625 + T2 = 93.75 + 0.140625 Reorder the terms: 0.140625 + -0.75T + T2 = 93.75 + 0.140625 Combine like terms: 93.75 + 0.140625 = 93.890625 0.140625 + -0.75T + T2 = 93.890625 Factor a perfect square on the left side: (T + -0.375)(T + -0.375) = 93.890625 Calculate the square root of the right side: 9.689717488 Break this problem into two subproblems by setting (T + -0.375) equal to 9.689717488 and -9.689717488.Subproblem 1
T + -0.375 = 9.689717488 Simplifying T + -0.375 = 9.689717488 Reorder the terms: -0.375 + T = 9.689717488 Solving -0.375 + T = 9.689717488 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + T = 9.689717488 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + T = 9.689717488 + 0.375 T = 9.689717488 + 0.375 Combine like terms: 9.689717488 + 0.375 = 10.064717488 T = 10.064717488 Simplifying T = 10.064717488Subproblem 2
T + -0.375 = -9.689717488 Simplifying T + -0.375 = -9.689717488 Reorder the terms: -0.375 + T = -9.689717488 Solving -0.375 + T = -9.689717488 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + T = -9.689717488 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + T = -9.689717488 + 0.375 T = -9.689717488 + 0.375 Combine like terms: -9.689717488 + 0.375 = -9.314717488 T = -9.314717488 Simplifying T = -9.314717488Solution
The solution to the problem is based on the solutions from the subproblems. T = {10.064717488, -9.314717488}
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