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Simplifying 1.25t2 + 2.1t + -50.0 = 0 Reorder the terms: -50.0 + 2.1t + 1.25t2 = 0 Solving -50.0 + 2.1t + 1.25t2 = 0 Solving for variable 't'. 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 = 5.540094043 t = 5.540094043 Simplifying t = 5.540094043Subproblem 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 = -7.220094043 t = -7.220094043 Simplifying t = -7.220094043Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.540094043, -7.220094043}
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