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Simplifying 22x2 + 127x + 3 = 0 Reorder the terms: 3 + 127x + 22x2 = 0 Solving 3 + 127x + 22x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 22 the coefficient of the squared term: Divide each side by '22'. 0.1363636364 + 5.772727273x + x2 = 0 Move the constant term to the right: Add '-0.1363636364' to each side of the equation. 0.1363636364 + 5.772727273x + -0.1363636364 + x2 = 0 + -0.1363636364 Reorder the terms: 0.1363636364 + -0.1363636364 + 5.772727273x + x2 = 0 + -0.1363636364 Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000 0.0000000000 + 5.772727273x + x2 = 0 + -0.1363636364 5.772727273x + x2 = 0 + -0.1363636364 Combine like terms: 0 + -0.1363636364 = -0.1363636364 5.772727273x + x2 = -0.1363636364 The x term is 5.772727273x. Take half its coefficient (2.886363637). Square it (8.331095045) and add it to both sides. Add '8.331095045' to each side of the equation. 5.772727273x + 8.331095045 + x2 = -0.1363636364 + 8.331095045 Reorder the terms: 8.331095045 + 5.772727273x + x2 = -0.1363636364 + 8.331095045 Combine like terms: -0.1363636364 + 8.331095045 = 8.1947314086 8.331095045 + 5.772727273x + x2 = 8.1947314086 Factor a perfect square on the left side: (x + 2.886363637)(x + 2.886363637) = 8.1947314086 Calculate the square root of the right side: 2.862644129 Break this problem into two subproblems by setting (x + 2.886363637) equal to 2.862644129 and -2.862644129.Subproblem 1
x + 2.886363637 = 2.862644129 Simplifying x + 2.886363637 = 2.862644129 Reorder the terms: 2.886363637 + x = 2.862644129 Solving 2.886363637 + x = 2.862644129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.886363637' to each side of the equation. 2.886363637 + -2.886363637 + x = 2.862644129 + -2.886363637 Combine like terms: 2.886363637 + -2.886363637 = 0.000000000 0.000000000 + x = 2.862644129 + -2.886363637 x = 2.862644129 + -2.886363637 Combine like terms: 2.862644129 + -2.886363637 = -0.023719508 x = -0.023719508 Simplifying x = -0.023719508Subproblem 2
x + 2.886363637 = -2.862644129 Simplifying x + 2.886363637 = -2.862644129 Reorder the terms: 2.886363637 + x = -2.862644129 Solving 2.886363637 + x = -2.862644129 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.886363637' to each side of the equation. 2.886363637 + -2.886363637 + x = -2.862644129 + -2.886363637 Combine like terms: 2.886363637 + -2.886363637 = 0.000000000 0.000000000 + x = -2.862644129 + -2.886363637 x = -2.862644129 + -2.886363637 Combine like terms: -2.862644129 + -2.886363637 = -5.749007766 x = -5.749007766 Simplifying x = -5.749007766Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.023719508, -5.749007766}
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