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Simplifying 2.066 = 9t + -9.8t2 Solving 2.066 = 9t + -9.8t2 Solving for variable 't'. Reorder the terms: 2.066 + -9t + 9.8t2 = 9t + -9t + -9.8t2 + 9.8t2 Combine like terms: 9t + -9t = 0 2.066 + -9t + 9.8t2 = 0 + -9.8t2 + 9.8t2 2.066 + -9t + 9.8t2 = -9.8t2 + 9.8t2 Combine like terms: -9.8t2 + 9.8t2 = 0.0 2.066 + -9t + 9.8t2 = 0.0 Begin completing the square. Divide all terms by 9.8 the coefficient of the squared term: Divide each side by '9.8'. 0.2108163265 + -0.9183673469t + t2 = 0 Move the constant term to the right: Add '-0.2108163265' to each side of the equation. 0.2108163265 + -0.9183673469t + -0.2108163265 + t2 = 0 + -0.2108163265 Reorder the terms: 0.2108163265 + -0.2108163265 + -0.9183673469t + t2 = 0 + -0.2108163265 Combine like terms: 0.2108163265 + -0.2108163265 = 0.0000000000 0.0000000000 + -0.9183673469t + t2 = 0 + -0.2108163265 -0.9183673469t + t2 = 0 + -0.2108163265 Combine like terms: 0 + -0.2108163265 = -0.2108163265 -0.9183673469t + t2 = -0.2108163265 The t term is -0.9183673469t. Take half its coefficient (-0.4591836735). Square it (0.2108496460) and add it to both sides. Add '0.2108496460' to each side of the equation. -0.9183673469t + 0.2108496460 + t2 = -0.2108163265 + 0.2108496460 Reorder the terms: 0.2108496460 + -0.9183673469t + t2 = -0.2108163265 + 0.2108496460 Combine like terms: -0.2108163265 + 0.2108496460 = 0.0000333195 0.2108496460 + -0.9183673469t + t2 = 0.0000333195 Factor a perfect square on the left side: (t + -0.4591836735)(t + -0.4591836735) = 0.0000333195 Calculate the square root of the right side: 0.005772305 Break this problem into two subproblems by setting (t + -0.4591836735) equal to 0.005772305 and -0.005772305.Subproblem 1
t + -0.4591836735 = 0.005772305 Simplifying t + -0.4591836735 = 0.005772305 Reorder the terms: -0.4591836735 + t = 0.005772305 Solving -0.4591836735 + t = 0.005772305 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4591836735' to each side of the equation. -0.4591836735 + 0.4591836735 + t = 0.005772305 + 0.4591836735 Combine like terms: -0.4591836735 + 0.4591836735 = 0.0000000000 0.0000000000 + t = 0.005772305 + 0.4591836735 t = 0.005772305 + 0.4591836735 Combine like terms: 0.005772305 + 0.4591836735 = 0.4649559785 t = 0.4649559785 Simplifying t = 0.4649559785Subproblem 2
t + -0.4591836735 = -0.005772305 Simplifying t + -0.4591836735 = -0.005772305 Reorder the terms: -0.4591836735 + t = -0.005772305 Solving -0.4591836735 + t = -0.005772305 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4591836735' to each side of the equation. -0.4591836735 + 0.4591836735 + t = -0.005772305 + 0.4591836735 Combine like terms: -0.4591836735 + 0.4591836735 = 0.0000000000 0.0000000000 + t = -0.005772305 + 0.4591836735 t = -0.005772305 + 0.4591836735 Combine like terms: -0.005772305 + 0.4591836735 = 0.4534113685 t = 0.4534113685 Simplifying t = 0.4534113685Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.4649559785, 0.4534113685}
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