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Simplifying -5 = 8.5t + -5t2 Solving -5 = 8.5t + -5t2 Solving for variable 't'. Reorder the terms: -5 + -8.5t + 5t2 = 8.5t + -8.5t + -5t2 + 5t2 Combine like terms: 8.5t + -8.5t = 0.0 -5 + -8.5t + 5t2 = 0.0 + -5t2 + 5t2 -5 + -8.5t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -5 + -8.5t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1 + -1.7t + t2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.7t + 1 + t2 = 0 + 1 Reorder the terms: -1 + 1 + -1.7t + t2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.7t + t2 = 0 + 1 -1.7t + t2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.7t + t2 = 1 The t term is -1.7t. Take half its coefficient (-0.85). Square it (0.7225) and add it to both sides. Add '0.7225' to each side of the equation. -1.7t + 0.7225 + t2 = 1 + 0.7225 Reorder the terms: 0.7225 + -1.7t + t2 = 1 + 0.7225 Combine like terms: 1 + 0.7225 = 1.7225 0.7225 + -1.7t + t2 = 1.7225 Factor a perfect square on the left side: (t + -0.85)(t + -0.85) = 1.7225 Calculate the square root of the right side: 1.312440475 Break this problem into two subproblems by setting (t + -0.85) equal to 1.312440475 and -1.312440475.Subproblem 1
t + -0.85 = 1.312440475 Simplifying t + -0.85 = 1.312440475 Reorder the terms: -0.85 + t = 1.312440475 Solving -0.85 + t = 1.312440475 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.85' to each side of the equation. -0.85 + 0.85 + t = 1.312440475 + 0.85 Combine like terms: -0.85 + 0.85 = 0.00 0.00 + t = 1.312440475 + 0.85 t = 1.312440475 + 0.85 Combine like terms: 1.312440475 + 0.85 = 2.162440475 t = 2.162440475 Simplifying t = 2.162440475Subproblem 2
t + -0.85 = -1.312440475 Simplifying t + -0.85 = -1.312440475 Reorder the terms: -0.85 + t = -1.312440475 Solving -0.85 + t = -1.312440475 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.85' to each side of the equation. -0.85 + 0.85 + t = -1.312440475 + 0.85 Combine like terms: -0.85 + 0.85 = 0.00 0.00 + t = -1.312440475 + 0.85 t = -1.312440475 + 0.85 Combine like terms: -1.312440475 + 0.85 = -0.462440475 t = -0.462440475 Simplifying t = -0.462440475Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.162440475, -0.462440475}
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