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Simplifying x2 + 53x + -2 = 0 Reorder the terms: -2 + 53x + x2 = 0 Solving -2 + 53x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 53x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 53x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 53x + x2 = 0 + 2 53x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 53x + x2 = 2 The x term is 53x. Take half its coefficient (26.5). Square it (702.25) and add it to both sides. Add '702.25' to each side of the equation. 53x + 702.25 + x2 = 2 + 702.25 Reorder the terms: 702.25 + 53x + x2 = 2 + 702.25 Combine like terms: 2 + 702.25 = 704.25 702.25 + 53x + x2 = 704.25 Factor a perfect square on the left side: (x + 26.5)(x + 26.5) = 704.25 Calculate the square root of the right side: 26.537709019 Break this problem into two subproblems by setting (x + 26.5) equal to 26.537709019 and -26.537709019.Subproblem 1
x + 26.5 = 26.537709019 Simplifying x + 26.5 = 26.537709019 Reorder the terms: 26.5 + x = 26.537709019 Solving 26.5 + x = 26.537709019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-26.5' to each side of the equation. 26.5 + -26.5 + x = 26.537709019 + -26.5 Combine like terms: 26.5 + -26.5 = 0.0 0.0 + x = 26.537709019 + -26.5 x = 26.537709019 + -26.5 Combine like terms: 26.537709019 + -26.5 = 0.037709019 x = 0.037709019 Simplifying x = 0.037709019Subproblem 2
x + 26.5 = -26.537709019 Simplifying x + 26.5 = -26.537709019 Reorder the terms: 26.5 + x = -26.537709019 Solving 26.5 + x = -26.537709019 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-26.5' to each side of the equation. 26.5 + -26.5 + x = -26.537709019 + -26.5 Combine like terms: 26.5 + -26.5 = 0.0 0.0 + x = -26.537709019 + -26.5 x = -26.537709019 + -26.5 Combine like terms: -26.537709019 + -26.5 = -53.037709019 x = -53.037709019 Simplifying x = -53.037709019Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.037709019, -53.037709019}
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