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Simplifying x2 + 11x + -26 = 2x + 22 Reorder the terms: -26 + 11x + x2 = 2x + 22 Reorder the terms: -26 + 11x + x2 = 22 + 2x Solving -26 + 11x + x2 = 22 + 2x Solving for variable 'x'. Reorder the terms: -26 + -22 + 11x + -2x + x2 = 22 + 2x + -22 + -2x Combine like terms: -26 + -22 = -48 -48 + 11x + -2x + x2 = 22 + 2x + -22 + -2x Combine like terms: 11x + -2x = 9x -48 + 9x + x2 = 22 + 2x + -22 + -2x Reorder the terms: -48 + 9x + x2 = 22 + -22 + 2x + -2x Combine like terms: 22 + -22 = 0 -48 + 9x + x2 = 0 + 2x + -2x -48 + 9x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -48 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + 9x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + 9x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + 9x + x2 = 0 + 48 9x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 9x + x2 = 48 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 48 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 48 + 20.25 Combine like terms: 48 + 20.25 = 68.25 20.25 + 9x + x2 = 68.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 68.25 Calculate the square root of the right side: 8.261355821 Break this problem into two subproblems by setting (x + 4.5) equal to 8.261355821 and -8.261355821.Subproblem 1
x + 4.5 = 8.261355821 Simplifying x + 4.5 = 8.261355821 Reorder the terms: 4.5 + x = 8.261355821 Solving 4.5 + x = 8.261355821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 8.261355821 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 8.261355821 + -4.5 x = 8.261355821 + -4.5 Combine like terms: 8.261355821 + -4.5 = 3.761355821 x = 3.761355821 Simplifying x = 3.761355821Subproblem 2
x + 4.5 = -8.261355821 Simplifying x + 4.5 = -8.261355821 Reorder the terms: 4.5 + x = -8.261355821 Solving 4.5 + x = -8.261355821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -8.261355821 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -8.261355821 + -4.5 x = -8.261355821 + -4.5 Combine like terms: -8.261355821 + -4.5 = -12.761355821 x = -12.761355821 Simplifying x = -12.761355821Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.761355821, -12.761355821}
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