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Simplifying 0 = 10 + 2t + -4.9t2 Solving 0 = 10 + 2t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -10 = -10 -10 + -2t + 4.9t2 = 10 + 2t + -4.9t2 + -10 + -2t + 4.9t2 Reorder the terms: -10 + -2t + 4.9t2 = 10 + -10 + 2t + -2t + -4.9t2 + 4.9t2 Combine like terms: 10 + -10 = 0 -10 + -2t + 4.9t2 = 0 + 2t + -2t + -4.9t2 + 4.9t2 -10 + -2t + 4.9t2 = 2t + -2t + -4.9t2 + 4.9t2 Combine like terms: 2t + -2t = 0 -10 + -2t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -10 + -2t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -10 + -2t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -2.040816327 + -0.4081632653t + t2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + -0.4081632653t + 2.040816327 + t2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + -0.4081632653t + t2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + -0.4081632653t + t2 = 0 + 2.040816327 -0.4081632653t + t2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 -0.4081632653t + t2 = 2.040816327 The t term is -0.4081632653t. Take half its coefficient (-0.2040816327). Square it (0.04164931281) and add it to both sides. Add '0.04164931281' to each side of the equation. -0.4081632653t + 0.04164931281 + t2 = 2.040816327 + 0.04164931281 Reorder the terms: 0.04164931281 + -0.4081632653t + t2 = 2.040816327 + 0.04164931281 Combine like terms: 2.040816327 + 0.04164931281 = 2.08246563981 0.04164931281 + -0.4081632653t + t2 = 2.08246563981 Factor a perfect square on the left side: (t + -0.2040816327)(t + -0.2040816327) = 2.08246563981 Calculate the square root of the right side: 1.443075064 Break this problem into two subproblems by setting (t + -0.2040816327) equal to 1.443075064 and -1.443075064.Subproblem 1
t + -0.2040816327 = 1.443075064 Simplifying t + -0.2040816327 = 1.443075064 Reorder the terms: -0.2040816327 + t = 1.443075064 Solving -0.2040816327 + t = 1.443075064 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2040816327' to each side of the equation. -0.2040816327 + 0.2040816327 + t = 1.443075064 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + t = 1.443075064 + 0.2040816327 t = 1.443075064 + 0.2040816327 Combine like terms: 1.443075064 + 0.2040816327 = 1.6471566967 t = 1.6471566967 Simplifying t = 1.6471566967Subproblem 2
t + -0.2040816327 = -1.443075064 Simplifying t + -0.2040816327 = -1.443075064 Reorder the terms: -0.2040816327 + t = -1.443075064 Solving -0.2040816327 + t = -1.443075064 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2040816327' to each side of the equation. -0.2040816327 + 0.2040816327 + t = -1.443075064 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + t = -1.443075064 + 0.2040816327 t = -1.443075064 + 0.2040816327 Combine like terms: -1.443075064 + 0.2040816327 = -1.2389934313 t = -1.2389934313 Simplifying t = -1.2389934313Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.6471566967, -1.2389934313}
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