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Simplifying -9.8t2 + 4.9t + 10 = 0 Reorder the terms: 10 + 4.9t + -9.8t2 = 0 Solving 10 + 4.9t + -9.8t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -9.8 the coefficient of the squared term: Divide each side by '-9.8'. -1.020408163 + -0.5t + t2 = 0 Move the constant term to the right: Add '1.020408163' to each side of the equation. -1.020408163 + -0.5t + 1.020408163 + t2 = 0 + 1.020408163 Reorder the terms: -1.020408163 + 1.020408163 + -0.5t + t2 = 0 + 1.020408163 Combine like terms: -1.020408163 + 1.020408163 = 0.000000000 0.000000000 + -0.5t + t2 = 0 + 1.020408163 -0.5t + t2 = 0 + 1.020408163 Combine like terms: 0 + 1.020408163 = 1.020408163 -0.5t + t2 = 1.020408163 The t term is -0.5t. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5t + 0.0625 + t2 = 1.020408163 + 0.0625 Reorder the terms: 0.0625 + -0.5t + t2 = 1.020408163 + 0.0625 Combine like terms: 1.020408163 + 0.0625 = 1.082908163 0.0625 + -0.5t + t2 = 1.082908163 Factor a perfect square on the left side: (t + -0.25)(t + -0.25) = 1.082908163 Calculate the square root of the right side: 1.040628734 Break this problem into two subproblems by setting (t + -0.25) equal to 1.040628734 and -1.040628734.Subproblem 1
t + -0.25 = 1.040628734 Simplifying t + -0.25 = 1.040628734 Reorder the terms: -0.25 + t = 1.040628734 Solving -0.25 + t = 1.040628734 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + t = 1.040628734 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = 1.040628734 + 0.25 t = 1.040628734 + 0.25 Combine like terms: 1.040628734 + 0.25 = 1.290628734 t = 1.290628734 Simplifying t = 1.290628734Subproblem 2
t + -0.25 = -1.040628734 Simplifying t + -0.25 = -1.040628734 Reorder the terms: -0.25 + t = -1.040628734 Solving -0.25 + t = -1.040628734 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + t = -1.040628734 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + t = -1.040628734 + 0.25 t = -1.040628734 + 0.25 Combine like terms: -1.040628734 + 0.25 = -0.790628734 t = -0.790628734 Simplifying t = -0.790628734Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.290628734, -0.790628734}
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