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Simplifying t2 + -133t + -1975 = 0 Reorder the terms: -1975 + -133t + t2 = 0 Solving -1975 + -133t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '1975' to each side of the equation. -1975 + -133t + 1975 + t2 = 0 + 1975 Reorder the terms: -1975 + 1975 + -133t + t2 = 0 + 1975 Combine like terms: -1975 + 1975 = 0 0 + -133t + t2 = 0 + 1975 -133t + t2 = 0 + 1975 Combine like terms: 0 + 1975 = 1975 -133t + t2 = 1975 The t term is -133t. Take half its coefficient (-66.5). Square it (4422.25) and add it to both sides. Add '4422.25' to each side of the equation. -133t + 4422.25 + t2 = 1975 + 4422.25 Reorder the terms: 4422.25 + -133t + t2 = 1975 + 4422.25 Combine like terms: 1975 + 4422.25 = 6397.25 4422.25 + -133t + t2 = 6397.25 Factor a perfect square on the left side: (t + -66.5)(t + -66.5) = 6397.25 Calculate the square root of the right side: 79.982810653 Break this problem into two subproblems by setting (t + -66.5) equal to 79.982810653 and -79.982810653.Subproblem 1
t + -66.5 = 79.982810653 Simplifying t + -66.5 = 79.982810653 Reorder the terms: -66.5 + t = 79.982810653 Solving -66.5 + t = 79.982810653 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '66.5' to each side of the equation. -66.5 + 66.5 + t = 79.982810653 + 66.5 Combine like terms: -66.5 + 66.5 = 0.0 0.0 + t = 79.982810653 + 66.5 t = 79.982810653 + 66.5 Combine like terms: 79.982810653 + 66.5 = 146.482810653 t = 146.482810653 Simplifying t = 146.482810653Subproblem 2
t + -66.5 = -79.982810653 Simplifying t + -66.5 = -79.982810653 Reorder the terms: -66.5 + t = -79.982810653 Solving -66.5 + t = -79.982810653 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '66.5' to each side of the equation. -66.5 + 66.5 + t = -79.982810653 + 66.5 Combine like terms: -66.5 + 66.5 = 0.0 0.0 + t = -79.982810653 + 66.5 t = -79.982810653 + 66.5 Combine like terms: -79.982810653 + 66.5 = -13.482810653 t = -13.482810653 Simplifying t = -13.482810653Solution
The solution to the problem is based on the solutions from the subproblems. t = {146.482810653, -13.482810653}
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