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Simplifying 0 = 0.4t2 + -7.7t + 0.5 Reorder the terms: 0 = 0.5 + -7.7t + 0.4t2 Solving 0 = 0.5 + -7.7t + 0.4t2 Solving for variable 't'. Combine like terms: 0 + -0.5 = -0.5 -0.5 + 7.7t + -0.4t2 = 0.5 + -7.7t + 0.4t2 + -0.5 + 7.7t + -0.4t2 Reorder the terms: -0.5 + 7.7t + -0.4t2 = 0.5 + -0.5 + -7.7t + 7.7t + 0.4t2 + -0.4t2 Combine like terms: 0.5 + -0.5 = 0.0 -0.5 + 7.7t + -0.4t2 = 0.0 + -7.7t + 7.7t + 0.4t2 + -0.4t2 -0.5 + 7.7t + -0.4t2 = -7.7t + 7.7t + 0.4t2 + -0.4t2 Combine like terms: -7.7t + 7.7t = 0.0 -0.5 + 7.7t + -0.4t2 = 0.0 + 0.4t2 + -0.4t2 -0.5 + 7.7t + -0.4t2 = 0.4t2 + -0.4t2 Combine like terms: 0.4t2 + -0.4t2 = 0.0 -0.5 + 7.7t + -0.4t2 = 0.0 Begin completing the square. Divide all terms by -0.4 the coefficient of the squared term: Divide each side by '-0.4'. 1.25 + -19.25t + t2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -19.25t + -1.25 + t2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -19.25t + t2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -19.25t + t2 = 0 + -1.25 -19.25t + t2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -19.25t + t2 = -1.25 The t term is -19.25t. Take half its coefficient (-9.625). Square it (92.640625) and add it to both sides. Add '92.640625' to each side of the equation. -19.25t + 92.640625 + t2 = -1.25 + 92.640625 Reorder the terms: 92.640625 + -19.25t + t2 = -1.25 + 92.640625 Combine like terms: -1.25 + 92.640625 = 91.390625 92.640625 + -19.25t + t2 = 91.390625 Factor a perfect square on the left side: (t + -9.625)(t + -9.625) = 91.390625 Calculate the square root of the right side: 9.559844403 Break this problem into two subproblems by setting (t + -9.625) equal to 9.559844403 and -9.559844403.Subproblem 1
t + -9.625 = 9.559844403 Simplifying t + -9.625 = 9.559844403 Reorder the terms: -9.625 + t = 9.559844403 Solving -9.625 + t = 9.559844403 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.625' to each side of the equation. -9.625 + 9.625 + t = 9.559844403 + 9.625 Combine like terms: -9.625 + 9.625 = 0.000 0.000 + t = 9.559844403 + 9.625 t = 9.559844403 + 9.625 Combine like terms: 9.559844403 + 9.625 = 19.184844403 t = 19.184844403 Simplifying t = 19.184844403Subproblem 2
t + -9.625 = -9.559844403 Simplifying t + -9.625 = -9.559844403 Reorder the terms: -9.625 + t = -9.559844403 Solving -9.625 + t = -9.559844403 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.625' to each side of the equation. -9.625 + 9.625 + t = -9.559844403 + 9.625 Combine like terms: -9.625 + 9.625 = 0.000 0.000 + t = -9.559844403 + 9.625 t = -9.559844403 + 9.625 Combine like terms: -9.559844403 + 9.625 = 0.065155597 t = 0.065155597 Simplifying t = 0.065155597Solution
The solution to the problem is based on the solutions from the subproblems. t = {19.184844403, 0.065155597}
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