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Simplifying -1t2 + 1t + 3 = 0 Reorder the terms: 3 + 1t + -1t2 = 0 Solving 3 + 1t + -1t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + -1t + t2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -1t + 3 + t2 = 0 + 3 Reorder the terms: -3 + 3 + -1t + t2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1t + t2 = 0 + 3 -1t + t2 = 0 + 3 Combine like terms: 0 + 3 = 3 -1t + t2 = 3 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 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 3 + 0.25 Combine like terms: 3 + 0.25 = 3.25 0.25 + -1t + t2 = 3.25 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (t + -0.5) equal to 1.802775638 and -1.802775638.Subproblem 1
t + -0.5 = 1.802775638 Simplifying t + -0.5 = 1.802775638 Reorder the terms: -0.5 + t = 1.802775638 Solving -0.5 + t = 1.802775638 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 = 1.802775638 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 1.802775638 + 0.5 t = 1.802775638 + 0.5 Combine like terms: 1.802775638 + 0.5 = 2.302775638 t = 2.302775638 Simplifying t = 2.302775638Subproblem 2
t + -0.5 = -1.802775638 Simplifying t + -0.5 = -1.802775638 Reorder the terms: -0.5 + t = -1.802775638 Solving -0.5 + t = -1.802775638 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 = -1.802775638 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -1.802775638 + 0.5 t = -1.802775638 + 0.5 Combine like terms: -1.802775638 + 0.5 = -1.302775638 t = -1.302775638 Simplifying t = -1.302775638Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.302775638, -1.302775638}
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