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Simplifying 17 = 2t2 + -3t Reorder the terms: 17 = -3t + 2t2 Solving 17 = -3t + 2t2 Solving for variable 't'. Reorder the terms: 17 + 3t + -2t2 = -3t + 3t + 2t2 + -2t2 Combine like terms: -3t + 3t = 0 17 + 3t + -2t2 = 0 + 2t2 + -2t2 17 + 3t + -2t2 = 2t2 + -2t2 Combine like terms: 2t2 + -2t2 = 0 17 + 3t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -8.5 + -1.5t + t2 = 0 Move the constant term to the right: Add '8.5' to each side of the equation. -8.5 + -1.5t + 8.5 + t2 = 0 + 8.5 Reorder the terms: -8.5 + 8.5 + -1.5t + t2 = 0 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + -1.5t + t2 = 0 + 8.5 -1.5t + t2 = 0 + 8.5 Combine like terms: 0 + 8.5 = 8.5 -1.5t + t2 = 8.5 The t term is -1.5t. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5t + 0.5625 + t2 = 8.5 + 0.5625 Reorder the terms: 0.5625 + -1.5t + t2 = 8.5 + 0.5625 Combine like terms: 8.5 + 0.5625 = 9.0625 0.5625 + -1.5t + t2 = 9.0625 Factor a perfect square on the left side: (t + -0.75)(t + -0.75) = 9.0625 Calculate the square root of the right side: 3.010398645 Break this problem into two subproblems by setting (t + -0.75) equal to 3.010398645 and -3.010398645.Subproblem 1
t + -0.75 = 3.010398645 Simplifying t + -0.75 = 3.010398645 Reorder the terms: -0.75 + t = 3.010398645 Solving -0.75 + t = 3.010398645 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + t = 3.010398645 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + t = 3.010398645 + 0.75 t = 3.010398645 + 0.75 Combine like terms: 3.010398645 + 0.75 = 3.760398645 t = 3.760398645 Simplifying t = 3.760398645Subproblem 2
t + -0.75 = -3.010398645 Simplifying t + -0.75 = -3.010398645 Reorder the terms: -0.75 + t = -3.010398645 Solving -0.75 + t = -3.010398645 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + t = -3.010398645 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + t = -3.010398645 + 0.75 t = -3.010398645 + 0.75 Combine like terms: -3.010398645 + 0.75 = -2.260398645 t = -2.260398645 Simplifying t = -2.260398645Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.760398645, -2.260398645}
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