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Simplifying t2 + 80t = 68 Reorder the terms: 80t + t2 = 68 Solving 80t + t2 = 68 Solving for variable 't'. Reorder the terms: -68 + 80t + t2 = 68 + -68 Combine like terms: 68 + -68 = 0 -68 + 80t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '68' to each side of the equation. -68 + 80t + 68 + t2 = 0 + 68 Reorder the terms: -68 + 68 + 80t + t2 = 0 + 68 Combine like terms: -68 + 68 = 0 0 + 80t + t2 = 0 + 68 80t + t2 = 0 + 68 Combine like terms: 0 + 68 = 68 80t + t2 = 68 The t term is 80t. Take half its coefficient (40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. 80t + 1600 + t2 = 68 + 1600 Reorder the terms: 1600 + 80t + t2 = 68 + 1600 Combine like terms: 68 + 1600 = 1668 1600 + 80t + t2 = 1668 Factor a perfect square on the left side: (t + 40)(t + 40) = 1668 Calculate the square root of the right side: 40.841155713 Break this problem into two subproblems by setting (t + 40) equal to 40.841155713 and -40.841155713.Subproblem 1
t + 40 = 40.841155713 Simplifying t + 40 = 40.841155713 Reorder the terms: 40 + t = 40.841155713 Solving 40 + t = 40.841155713 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + t = 40.841155713 + -40 Combine like terms: 40 + -40 = 0 0 + t = 40.841155713 + -40 t = 40.841155713 + -40 Combine like terms: 40.841155713 + -40 = 0.841155713 t = 0.841155713 Simplifying t = 0.841155713Subproblem 2
t + 40 = -40.841155713 Simplifying t + 40 = -40.841155713 Reorder the terms: 40 + t = -40.841155713 Solving 40 + t = -40.841155713 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + t = -40.841155713 + -40 Combine like terms: 40 + -40 = 0 0 + t = -40.841155713 + -40 t = -40.841155713 + -40 Combine like terms: -40.841155713 + -40 = -80.841155713 t = -80.841155713 Simplifying t = -80.841155713Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.841155713, -80.841155713}
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