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Simplifying 3t2 + -3t + -10 = 0 Reorder the terms: -10 + -3t + 3t2 = 0 Solving -10 + -3t + 3t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3.333333333 + -1t + t2 = 0 Move the constant term to the right: Add '3.333333333' to each side of the equation. -3.333333333 + -1t + 3.333333333 + t2 = 0 + 3.333333333 Reorder the terms: -3.333333333 + 3.333333333 + -1t + t2 = 0 + 3.333333333 Combine like terms: -3.333333333 + 3.333333333 = 0.000000000 0.000000000 + -1t + t2 = 0 + 3.333333333 -1t + t2 = 0 + 3.333333333 Combine like terms: 0 + 3.333333333 = 3.333333333 -1t + t2 = 3.333333333 The t term is -1t. 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. -1t + 0.25 + t2 = 3.333333333 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 3.333333333 + 0.25 Combine like terms: 3.333333333 + 0.25 = 3.583333333 0.25 + -1t + t2 = 3.583333333 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 3.583333333 Calculate the square root of the right side: 1.892969449 Break this problem into two subproblems by setting (t + -0.5) equal to 1.892969449 and -1.892969449.Subproblem 1
t + -0.5 = 1.892969449 Simplifying t + -0.5 = 1.892969449 Reorder the terms: -0.5 + t = 1.892969449 Solving -0.5 + t = 1.892969449 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 = 1.892969449 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 1.892969449 + 0.5 t = 1.892969449 + 0.5 Combine like terms: 1.892969449 + 0.5 = 2.392969449 t = 2.392969449 Simplifying t = 2.392969449Subproblem 2
t + -0.5 = -1.892969449 Simplifying t + -0.5 = -1.892969449 Reorder the terms: -0.5 + t = -1.892969449 Solving -0.5 + t = -1.892969449 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 = -1.892969449 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -1.892969449 + 0.5 t = -1.892969449 + 0.5 Combine like terms: -1.892969449 + 0.5 = -1.392969449 t = -1.392969449 Simplifying t = -1.392969449Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.392969449, -1.392969449}
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