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Simplifying t2 + -38t + -140 = 0 Reorder the terms: -140 + -38t + t2 = 0 Solving -140 + -38t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '140' to each side of the equation. -140 + -38t + 140 + t2 = 0 + 140 Reorder the terms: -140 + 140 + -38t + t2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + -38t + t2 = 0 + 140 -38t + t2 = 0 + 140 Combine like terms: 0 + 140 = 140 -38t + t2 = 140 The t term is -38t. Take half its coefficient (-19). Square it (361) and add it to both sides. Add '361' to each side of the equation. -38t + 361 + t2 = 140 + 361 Reorder the terms: 361 + -38t + t2 = 140 + 361 Combine like terms: 140 + 361 = 501 361 + -38t + t2 = 501 Factor a perfect square on the left side: (t + -19)(t + -19) = 501 Calculate the square root of the right side: 22.383029286 Break this problem into two subproblems by setting (t + -19) equal to 22.383029286 and -22.383029286.Subproblem 1
t + -19 = 22.383029286 Simplifying t + -19 = 22.383029286 Reorder the terms: -19 + t = 22.383029286 Solving -19 + t = 22.383029286 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + t = 22.383029286 + 19 Combine like terms: -19 + 19 = 0 0 + t = 22.383029286 + 19 t = 22.383029286 + 19 Combine like terms: 22.383029286 + 19 = 41.383029286 t = 41.383029286 Simplifying t = 41.383029286Subproblem 2
t + -19 = -22.383029286 Simplifying t + -19 = -22.383029286 Reorder the terms: -19 + t = -22.383029286 Solving -19 + t = -22.383029286 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + t = -22.383029286 + 19 Combine like terms: -19 + 19 = 0 0 + t = -22.383029286 + 19 t = -22.383029286 + 19 Combine like terms: -22.383029286 + 19 = -3.383029286 t = -3.383029286 Simplifying t = -3.383029286Solution
The solution to the problem is based on the solutions from the subproblems. t = {41.383029286, -3.383029286}
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