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Simplifying t2 + -1t + -5 = 0 Reorder the terms: -5 + -1t + t2 = 0 Solving -5 + -1t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -1t + 5 + t2 = 0 + 5 Reorder the terms: -5 + 5 + -1t + t2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1t + t2 = 0 + 5 -1t + t2 = 0 + 5 Combine like terms: 0 + 5 = 5 -1t + t2 = 5 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 = 5 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 5 + 0.25 Combine like terms: 5 + 0.25 = 5.25 0.25 + -1t + t2 = 5.25 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (t + -0.5) equal to 2.291287847 and -2.291287847.Subproblem 1
t + -0.5 = 2.291287847 Simplifying t + -0.5 = 2.291287847 Reorder the terms: -0.5 + t = 2.291287847 Solving -0.5 + t = 2.291287847 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 = 2.291287847 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 2.291287847 + 0.5 t = 2.291287847 + 0.5 Combine like terms: 2.291287847 + 0.5 = 2.791287847 t = 2.791287847 Simplifying t = 2.791287847Subproblem 2
t + -0.5 = -2.291287847 Simplifying t + -0.5 = -2.291287847 Reorder the terms: -0.5 + t = -2.291287847 Solving -0.5 + t = -2.291287847 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 = -2.291287847 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -2.291287847 + 0.5 t = -2.291287847 + 0.5 Combine like terms: -2.291287847 + 0.5 = -1.791287847 t = -1.791287847 Simplifying t = -1.791287847Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.791287847, -1.791287847}
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