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Simplifying x2 + 18x + 26 = -4x + 2 Reorder the terms: 26 + 18x + x2 = -4x + 2 Reorder the terms: 26 + 18x + x2 = 2 + -4x Solving 26 + 18x + x2 = 2 + -4x Solving for variable 'x'. Reorder the terms: 26 + -2 + 18x + 4x + x2 = 2 + -4x + -2 + 4x Combine like terms: 26 + -2 = 24 24 + 18x + 4x + x2 = 2 + -4x + -2 + 4x Combine like terms: 18x + 4x = 22x 24 + 22x + x2 = 2 + -4x + -2 + 4x Reorder the terms: 24 + 22x + x2 = 2 + -2 + -4x + 4x Combine like terms: 2 + -2 = 0 24 + 22x + x2 = 0 + -4x + 4x 24 + 22x + x2 = -4x + 4x Combine like terms: -4x + 4x = 0 24 + 22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-24' to each side of the equation. 24 + 22x + -24 + x2 = 0 + -24 Reorder the terms: 24 + -24 + 22x + x2 = 0 + -24 Combine like terms: 24 + -24 = 0 0 + 22x + x2 = 0 + -24 22x + x2 = 0 + -24 Combine like terms: 0 + -24 = -24 22x + x2 = -24 The x term is 22x. Take half its coefficient (11). Square it (121) and add it to both sides. Add '121' to each side of the equation. 22x + 121 + x2 = -24 + 121 Reorder the terms: 121 + 22x + x2 = -24 + 121 Combine like terms: -24 + 121 = 97 121 + 22x + x2 = 97 Factor a perfect square on the left side: (x + 11)(x + 11) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (x + 11) equal to 9.848857802 and -9.848857802.Subproblem 1
x + 11 = 9.848857802 Simplifying x + 11 = 9.848857802 Reorder the terms: 11 + x = 9.848857802 Solving 11 + x = 9.848857802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = 9.848857802 + -11 Combine like terms: 11 + -11 = 0 0 + x = 9.848857802 + -11 x = 9.848857802 + -11 Combine like terms: 9.848857802 + -11 = -1.151142198 x = -1.151142198 Simplifying x = -1.151142198Subproblem 2
x + 11 = -9.848857802 Simplifying x + 11 = -9.848857802 Reorder the terms: 11 + x = -9.848857802 Solving 11 + x = -9.848857802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + x = -9.848857802 + -11 Combine like terms: 11 + -11 = 0 0 + x = -9.848857802 + -11 x = -9.848857802 + -11 Combine like terms: -9.848857802 + -11 = -20.848857802 x = -20.848857802 Simplifying x = -20.848857802Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.151142198, -20.848857802}
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