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Simplifying t2 + -40t + -1950 = 0 Reorder the terms: -1950 + -40t + t2 = 0 Solving -1950 + -40t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '1950' to each side of the equation. -1950 + -40t + 1950 + t2 = 0 + 1950 Reorder the terms: -1950 + 1950 + -40t + t2 = 0 + 1950 Combine like terms: -1950 + 1950 = 0 0 + -40t + t2 = 0 + 1950 -40t + t2 = 0 + 1950 Combine like terms: 0 + 1950 = 1950 -40t + t2 = 1950 The t term is -40t. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40t + 400 + t2 = 1950 + 400 Reorder the terms: 400 + -40t + t2 = 1950 + 400 Combine like terms: 1950 + 400 = 2350 400 + -40t + t2 = 2350 Factor a perfect square on the left side: (t + -20)(t + -20) = 2350 Calculate the square root of the right side: 48.476798574 Break this problem into two subproblems by setting (t + -20) equal to 48.476798574 and -48.476798574.Subproblem 1
t + -20 = 48.476798574 Simplifying t + -20 = 48.476798574 Reorder the terms: -20 + t = 48.476798574 Solving -20 + t = 48.476798574 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + t = 48.476798574 + 20 Combine like terms: -20 + 20 = 0 0 + t = 48.476798574 + 20 t = 48.476798574 + 20 Combine like terms: 48.476798574 + 20 = 68.476798574 t = 68.476798574 Simplifying t = 68.476798574Subproblem 2
t + -20 = -48.476798574 Simplifying t + -20 = -48.476798574 Reorder the terms: -20 + t = -48.476798574 Solving -20 + t = -48.476798574 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + t = -48.476798574 + 20 Combine like terms: -20 + 20 = 0 0 + t = -48.476798574 + 20 t = -48.476798574 + 20 Combine like terms: -48.476798574 + 20 = -28.476798574 t = -28.476798574 Simplifying t = -28.476798574Solution
The solution to the problem is based on the solutions from the subproblems. t = {68.476798574, -28.476798574}
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