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Simplifying t2 + -1t + -22 = 0 Reorder the terms: -22 + -1t + t2 = 0 Solving -22 + -1t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + -1t + 22 + t2 = 0 + 22 Reorder the terms: -22 + 22 + -1t + t2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -1t + t2 = 0 + 22 -1t + t2 = 0 + 22 Combine like terms: 0 + 22 = 22 -1t + t2 = 22 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 = 22 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 22 + 0.25 Combine like terms: 22 + 0.25 = 22.25 0.25 + -1t + t2 = 22.25 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (t + -0.5) equal to 4.716990566 and -4.716990566.Subproblem 1
t + -0.5 = 4.716990566 Simplifying t + -0.5 = 4.716990566 Reorder the terms: -0.5 + t = 4.716990566 Solving -0.5 + t = 4.716990566 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 = 4.716990566 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 4.716990566 + 0.5 t = 4.716990566 + 0.5 Combine like terms: 4.716990566 + 0.5 = 5.216990566 t = 5.216990566 Simplifying t = 5.216990566Subproblem 2
t + -0.5 = -4.716990566 Simplifying t + -0.5 = -4.716990566 Reorder the terms: -0.5 + t = -4.716990566 Solving -0.5 + t = -4.716990566 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 = -4.716990566 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -4.716990566 + 0.5 t = -4.716990566 + 0.5 Combine like terms: -4.716990566 + 0.5 = -4.216990566 t = -4.216990566 Simplifying t = -4.216990566Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.216990566, -4.216990566}
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