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Simplifying 0.031 = t + t2 Solving 0.031 = t + t2 Solving for variable 't'. Reorder the terms: 0.031 + -1t + -1t2 = t + -1t + t2 + -1t2 Combine like terms: t + -1t = 0 0.031 + -1t + -1t2 = 0 + t2 + -1t2 0.031 + -1t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 0.031 + -1t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -0.031 + t + t2 = 0 Move the constant term to the right: Add '0.031' to each side of the equation. -0.031 + t + 0.031 + t2 = 0 + 0.031 Reorder the terms: -0.031 + 0.031 + t + t2 = 0 + 0.031 Combine like terms: -0.031 + 0.031 = 0.000 0.000 + t + t2 = 0 + 0.031 t + t2 = 0 + 0.031 Combine like terms: 0 + 0.031 = 0.031 t + t2 = 0.031 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 = 0.031 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = 0.031 + 0.25 Combine like terms: 0.031 + 0.25 = 0.281 1.25 + t2 = 0.281 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 0.281 Calculate the square root of the right side: 0.530094331 Break this problem into two subproblems by setting (t + 0.5) equal to 0.530094331 and -0.530094331.Subproblem 1
t + 0.5 = 0.530094331 Simplifying t + 0.5 = 0.530094331 Reorder the terms: 0.5 + t = 0.530094331 Solving 0.5 + t = 0.530094331 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 = 0.530094331 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 0.530094331 + -0.5 t = 0.530094331 + -0.5 Combine like terms: 0.530094331 + -0.5 = 0.030094331 t = 0.030094331 Simplifying t = 0.030094331Subproblem 2
t + 0.5 = -0.530094331 Simplifying t + 0.5 = -0.530094331 Reorder the terms: 0.5 + t = -0.530094331 Solving 0.5 + t = -0.530094331 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 = -0.530094331 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -0.530094331 + -0.5 t = -0.530094331 + -0.5 Combine like terms: -0.530094331 + -0.5 = -1.030094331 t = -1.030094331 Simplifying t = -1.030094331Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.030094331, -1.030094331}
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