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Simplifying 0 = -10t2 + 8t + 0.2 Reorder the terms: 0 = 0.2 + 8t + -10t2 Solving 0 = 0.2 + 8t + -10t2 Solving for variable 't'. Combine like terms: 0 + -0.2 = -0.2 -0.2 + -8t + 10t2 = 0.2 + 8t + -10t2 + -0.2 + -8t + 10t2 Reorder the terms: -0.2 + -8t + 10t2 = 0.2 + -0.2 + 8t + -8t + -10t2 + 10t2 Combine like terms: 0.2 + -0.2 = 0.0 -0.2 + -8t + 10t2 = 0.0 + 8t + -8t + -10t2 + 10t2 -0.2 + -8t + 10t2 = 8t + -8t + -10t2 + 10t2 Combine like terms: 8t + -8t = 0 -0.2 + -8t + 10t2 = 0 + -10t2 + 10t2 -0.2 + -8t + 10t2 = -10t2 + 10t2 Combine like terms: -10t2 + 10t2 = 0 -0.2 + -8t + 10t2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.02 + -0.8t + t2 = 0 Move the constant term to the right: Add '0.02' to each side of the equation. -0.02 + -0.8t + 0.02 + t2 = 0 + 0.02 Reorder the terms: -0.02 + 0.02 + -0.8t + t2 = 0 + 0.02 Combine like terms: -0.02 + 0.02 = 0.00 0.00 + -0.8t + t2 = 0 + 0.02 -0.8t + t2 = 0 + 0.02 Combine like terms: 0 + 0.02 = 0.02 -0.8t + t2 = 0.02 The t term is -0.8t. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8t + 0.16 + t2 = 0.02 + 0.16 Reorder the terms: 0.16 + -0.8t + t2 = 0.02 + 0.16 Combine like terms: 0.02 + 0.16 = 0.18 0.16 + -0.8t + t2 = 0.18 Factor a perfect square on the left side: (t + -0.4)(t + -0.4) = 0.18 Calculate the square root of the right side: 0.424264069 Break this problem into two subproblems by setting (t + -0.4) equal to 0.424264069 and -0.424264069.Subproblem 1
t + -0.4 = 0.424264069 Simplifying t + -0.4 = 0.424264069 Reorder the terms: -0.4 + t = 0.424264069 Solving -0.4 + t = 0.424264069 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + t = 0.424264069 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + t = 0.424264069 + 0.4 t = 0.424264069 + 0.4 Combine like terms: 0.424264069 + 0.4 = 0.824264069 t = 0.824264069 Simplifying t = 0.824264069Subproblem 2
t + -0.4 = -0.424264069 Simplifying t + -0.4 = -0.424264069 Reorder the terms: -0.4 + t = -0.424264069 Solving -0.4 + t = -0.424264069 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + t = -0.424264069 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + t = -0.424264069 + 0.4 t = -0.424264069 + 0.4 Combine like terms: -0.424264069 + 0.4 = -0.024264069 t = -0.024264069 Simplifying t = -0.024264069Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.824264069, -0.024264069}
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