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Simplifying x + x2 + (5 + -1x)(x + x) = 26 Combine like terms: x + x = 2x x + x2 + (5 + -1x)(2x) = 26 Remove parenthesis around (2x) x + x2 + (5 + -1x) * 2x = 26 Reorder the terms for easier multiplication: x + x2 + 2x(5 + -1x) = 26 x + x2 + (5 * 2x + -1x * 2x) = 26 x + x2 + (10x + -2x2) = 26 Reorder the terms: x + 10x + x2 + -2x2 = 26 Combine like terms: x + 10x = 11x 11x + x2 + -2x2 = 26 Combine like terms: x2 + -2x2 = -1x2 11x + -1x2 = 26 Solving 11x + -1x2 = 26 Solving for variable 'x'. Reorder the terms: -26 + 11x + -1x2 = 26 + -26 Combine like terms: 26 + -26 = 0 -26 + 11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 26 + -11x + x2 = 0 Move the constant term to the right: Add '-26' to each side of the equation. 26 + -11x + -26 + x2 = 0 + -26 Reorder the terms: 26 + -26 + -11x + x2 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + -11x + x2 = 0 + -26 -11x + x2 = 0 + -26 Combine like terms: 0 + -26 = -26 -11x + x2 = -26 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -26 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -26 + 30.25 Combine like terms: -26 + 30.25 = 4.25 30.25 + -11x + x2 = 4.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + -5.5) equal to 2.061552813 and -2.061552813.Subproblem 1
x + -5.5 = 2.061552813 Simplifying x + -5.5 = 2.061552813 Reorder the terms: -5.5 + x = 2.061552813 Solving -5.5 + x = 2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 2.061552813 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 2.061552813 + 5.5 x = 2.061552813 + 5.5 Combine like terms: 2.061552813 + 5.5 = 7.561552813 x = 7.561552813 Simplifying x = 7.561552813Subproblem 2
x + -5.5 = -2.061552813 Simplifying x + -5.5 = -2.061552813 Reorder the terms: -5.5 + x = -2.061552813 Solving -5.5 + x = -2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -2.061552813 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -2.061552813 + 5.5 x = -2.061552813 + 5.5 Combine like terms: -2.061552813 + 5.5 = 3.438447187 x = 3.438447187 Simplifying x = 3.438447187Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.561552813, 3.438447187}
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