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Simplifying 0 = 50.0 + 2.1t + -1.25t2 Solving 0 = 50.0 + 2.1t + -1.25t2 Solving for variable 't'. Combine like terms: 0 + -50.0 = -50 -50 + -2.1t + 1.25t2 = 50.0 + 2.1t + -1.25t2 + -50.0 + -2.1t + 1.25t2 Reorder the terms: -50 + -2.1t + 1.25t2 = 50.0 + -50.0 + 2.1t + -2.1t + -1.25t2 + 1.25t2 Combine like terms: 50.0 + -50.0 = 0.0 -50 + -2.1t + 1.25t2 = 0.0 + 2.1t + -2.1t + -1.25t2 + 1.25t2 -50 + -2.1t + 1.25t2 = 2.1t + -2.1t + -1.25t2 + 1.25t2 Combine like terms: 2.1t + -2.1t = 0.0 -50 + -2.1t + 1.25t2 = 0.0 + -1.25t2 + 1.25t2 -50 + -2.1t + 1.25t2 = -1.25t2 + 1.25t2 Combine like terms: -1.25t2 + 1.25t2 = 0.00 -50 + -2.1t + 1.25t2 = 0.00 Begin completing the square. Divide all terms by 1.25 the coefficient of the squared term: Divide each side by '1.25'. -40 + -1.68t + t2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + -1.68t + 40 + t2 = 0 + 40 Reorder the terms: -40 + 40 + -1.68t + t2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -1.68t + t2 = 0 + 40 -1.68t + t2 = 0 + 40 Combine like terms: 0 + 40 = 40 -1.68t + t2 = 40 The t term is -1.68t. Take half its coefficient (-0.84). Square it (0.7056) and add it to both sides. Add '0.7056' to each side of the equation. -1.68t + 0.7056 + t2 = 40 + 0.7056 Reorder the terms: 0.7056 + -1.68t + t2 = 40 + 0.7056 Combine like terms: 40 + 0.7056 = 40.7056 0.7056 + -1.68t + t2 = 40.7056 Factor a perfect square on the left side: (t + -0.84)(t + -0.84) = 40.7056 Calculate the square root of the right side: 6.380094043 Break this problem into two subproblems by setting (t + -0.84) equal to 6.380094043 and -6.380094043.Subproblem 1
t + -0.84 = 6.380094043 Simplifying t + -0.84 = 6.380094043 Reorder the terms: -0.84 + t = 6.380094043 Solving -0.84 + t = 6.380094043 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.84' to each side of the equation. -0.84 + 0.84 + t = 6.380094043 + 0.84 Combine like terms: -0.84 + 0.84 = 0.00 0.00 + t = 6.380094043 + 0.84 t = 6.380094043 + 0.84 Combine like terms: 6.380094043 + 0.84 = 7.220094043 t = 7.220094043 Simplifying t = 7.220094043Subproblem 2
t + -0.84 = -6.380094043 Simplifying t + -0.84 = -6.380094043 Reorder the terms: -0.84 + t = -6.380094043 Solving -0.84 + t = -6.380094043 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.84' to each side of the equation. -0.84 + 0.84 + t = -6.380094043 + 0.84 Combine like terms: -0.84 + 0.84 = 0.00 0.00 + t = -6.380094043 + 0.84 t = -6.380094043 + 0.84 Combine like terms: -6.380094043 + 0.84 = -5.540094043 t = -5.540094043 Simplifying t = -5.540094043Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.220094043, -5.540094043}
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