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Simplifying -1t2 + 4t + 33 = 0 Reorder the terms: 33 + 4t + -1t2 = 0 Solving 33 + 4t + -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'. -33 + -4t + t2 = 0 Move the constant term to the right: Add '33' to each side of the equation. -33 + -4t + 33 + t2 = 0 + 33 Reorder the terms: -33 + 33 + -4t + t2 = 0 + 33 Combine like terms: -33 + 33 = 0 0 + -4t + t2 = 0 + 33 -4t + t2 = 0 + 33 Combine like terms: 0 + 33 = 33 -4t + t2 = 33 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = 33 + 4 Reorder the terms: 4 + -4t + t2 = 33 + 4 Combine like terms: 33 + 4 = 37 4 + -4t + t2 = 37 Factor a perfect square on the left side: (t + -2)(t + -2) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (t + -2) equal to 6.08276253 and -6.08276253.Subproblem 1
t + -2 = 6.08276253 Simplifying t + -2 = 6.08276253 Reorder the terms: -2 + t = 6.08276253 Solving -2 + t = 6.08276253 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 6.08276253 + 2 Combine like terms: -2 + 2 = 0 0 + t = 6.08276253 + 2 t = 6.08276253 + 2 Combine like terms: 6.08276253 + 2 = 8.08276253 t = 8.08276253 Simplifying t = 8.08276253Subproblem 2
t + -2 = -6.08276253 Simplifying t + -2 = -6.08276253 Reorder the terms: -2 + t = -6.08276253 Solving -2 + t = -6.08276253 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -6.08276253 + 2 Combine like terms: -2 + 2 = 0 0 + t = -6.08276253 + 2 t = -6.08276253 + 2 Combine like terms: -6.08276253 + 2 = -4.08276253 t = -4.08276253 Simplifying t = -4.08276253Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.08276253, -4.08276253}
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