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Simplifying 8.688 = (t2) + t 8.688 = t2 + t Reorder the terms: 8.688 = t + t2 Solving 8.688 = t + t2 Solving for variable 't'. Reorder the terms: 8.688 + -1t + -1t2 = t + -1t + t2 + -1t2 Combine like terms: t + -1t = 0 8.688 + -1t + -1t2 = 0 + t2 + -1t2 8.688 + -1t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 8.688 + -1t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8.688 + t + t2 = 0 Move the constant term to the right: Add '8.688' to each side of the equation. -8.688 + t + 8.688 + t2 = 0 + 8.688 Reorder the terms: -8.688 + 8.688 + t + t2 = 0 + 8.688 Combine like terms: -8.688 + 8.688 = 0.000 0.000 + t + t2 = 0 + 8.688 t + t2 = 0 + 8.688 Combine like terms: 0 + 8.688 = 8.688 t + t2 = 8.688 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + t2 = 8.688 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = 8.688 + 0.25 Combine like terms: 8.688 + 0.25 = 8.938 1.25 + t2 = 8.938 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 8.938 Calculate the square root of the right side: 2.989648809 Break this problem into two subproblems by setting (t + 0.5) equal to 2.989648809 and -2.989648809.Subproblem 1
t + 0.5 = 2.989648809 Simplifying t + 0.5 = 2.989648809 Reorder the terms: 0.5 + t = 2.989648809 Solving 0.5 + t = 2.989648809 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 2.989648809 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 2.989648809 + -0.5 t = 2.989648809 + -0.5 Combine like terms: 2.989648809 + -0.5 = 2.489648809 t = 2.489648809 Simplifying t = 2.489648809Subproblem 2
t + 0.5 = -2.989648809 Simplifying t + 0.5 = -2.989648809 Reorder the terms: 0.5 + t = -2.989648809 Solving 0.5 + t = -2.989648809 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -2.989648809 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -2.989648809 + -0.5 t = -2.989648809 + -0.5 Combine like terms: -2.989648809 + -0.5 = -3.489648809 t = -3.489648809 Simplifying t = -3.489648809Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.489648809, -3.489648809}
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