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Simplifying -100 = -490t2 + 200t Reorder the terms: -100 = 200t + -490t2 Solving -100 = 200t + -490t2 Solving for variable 't'. Reorder the terms: -100 + -200t + 490t2 = 200t + -200t + -490t2 + 490t2 Combine like terms: 200t + -200t = 0 -100 + -200t + 490t2 = 0 + -490t2 + 490t2 -100 + -200t + 490t2 = -490t2 + 490t2 Combine like terms: -490t2 + 490t2 = 0 -100 + -200t + 490t2 = 0 Factor out the Greatest Common Factor (GCF), '10'. 10(-10 + -20t + 49t2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-10 + -20t + 49t2)' equal to zero and attempt to solve: Simplifying -10 + -20t + 49t2 = 0 Solving -10 + -20t + 49t2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.2040816327 + -0.4081632653t + t2 = 0 Move the constant term to the right: Add '0.2040816327' to each side of the equation. -0.2040816327 + -0.4081632653t + 0.2040816327 + t2 = 0 + 0.2040816327 Reorder the terms: -0.2040816327 + 0.2040816327 + -0.4081632653t + t2 = 0 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + -0.4081632653t + t2 = 0 + 0.2040816327 -0.4081632653t + t2 = 0 + 0.2040816327 Combine like terms: 0 + 0.2040816327 = 0.2040816327 -0.4081632653t + t2 = 0.2040816327 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 = 0.2040816327 + 0.04164931281 Reorder the terms: 0.04164931281 + -0.4081632653t + t2 = 0.2040816327 + 0.04164931281 Combine like terms: 0.2040816327 + 0.04164931281 = 0.24573094551 0.04164931281 + -0.4081632653t + t2 = 0.24573094551 Factor a perfect square on the left side: (t + -0.2040816327)(t + -0.2040816327) = 0.24573094551 Calculate the square root of the right side: 0.495712563 Break this problem into two subproblems by setting (t + -0.2040816327) equal to 0.495712563 and -0.495712563.Subproblem 1
t + -0.2040816327 = 0.495712563 Simplifying t + -0.2040816327 = 0.495712563 Reorder the terms: -0.2040816327 + t = 0.495712563 Solving -0.2040816327 + t = 0.495712563 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 = 0.495712563 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + t = 0.495712563 + 0.2040816327 t = 0.495712563 + 0.2040816327 Combine like terms: 0.495712563 + 0.2040816327 = 0.6997941957 t = 0.6997941957 Simplifying t = 0.6997941957Subproblem 2
t + -0.2040816327 = -0.495712563 Simplifying t + -0.2040816327 = -0.495712563 Reorder the terms: -0.2040816327 + t = -0.495712563 Solving -0.2040816327 + t = -0.495712563 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 = -0.495712563 + 0.2040816327 Combine like terms: -0.2040816327 + 0.2040816327 = 0.0000000000 0.0000000000 + t = -0.495712563 + 0.2040816327 t = -0.495712563 + 0.2040816327 Combine like terms: -0.495712563 + 0.2040816327 = -0.2916309303 t = -0.2916309303 Simplifying t = -0.2916309303Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.6997941957, -0.2916309303}Solution
t = {0.6997941957, -0.2916309303}
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