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Simplifying x + 2 = 2x(x + -13) Reorder the terms: 2 + x = 2x(x + -13) Reorder the terms: 2 + x = 2x(-13 + x) 2 + x = (-13 * 2x + x * 2x) 2 + x = (-26x + 2x2) Solving 2 + x = -26x + 2x2 Solving for variable 'x'. Combine like terms: x + 26x = 27x 2 + 27x + -2x2 = -26x + 2x2 + 26x + -2x2 Reorder the terms: 2 + 27x + -2x2 = -26x + 26x + 2x2 + -2x2 Combine like terms: -26x + 26x = 0 2 + 27x + -2x2 = 0 + 2x2 + -2x2 2 + 27x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 2 + 27x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -1 + -13.5x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -13.5x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -13.5x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -13.5x + x2 = 0 + 1 -13.5x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -13.5x + x2 = 1 The x term is -13.5x. Take half its coefficient (-6.75). Square it (45.5625) and add it to both sides. Add '45.5625' to each side of the equation. -13.5x + 45.5625 + x2 = 1 + 45.5625 Reorder the terms: 45.5625 + -13.5x + x2 = 1 + 45.5625 Combine like terms: 1 + 45.5625 = 46.5625 45.5625 + -13.5x + x2 = 46.5625 Factor a perfect square on the left side: (x + -6.75)(x + -6.75) = 46.5625 Calculate the square root of the right side: 6.823672032 Break this problem into two subproblems by setting (x + -6.75) equal to 6.823672032 and -6.823672032.Subproblem 1
x + -6.75 = 6.823672032 Simplifying x + -6.75 = 6.823672032 Reorder the terms: -6.75 + x = 6.823672032 Solving -6.75 + x = 6.823672032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + x = 6.823672032 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = 6.823672032 + 6.75 x = 6.823672032 + 6.75 Combine like terms: 6.823672032 + 6.75 = 13.573672032 x = 13.573672032 Simplifying x = 13.573672032Subproblem 2
x + -6.75 = -6.823672032 Simplifying x + -6.75 = -6.823672032 Reorder the terms: -6.75 + x = -6.823672032 Solving -6.75 + x = -6.823672032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.75' to each side of the equation. -6.75 + 6.75 + x = -6.823672032 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + x = -6.823672032 + 6.75 x = -6.823672032 + 6.75 Combine like terms: -6.823672032 + 6.75 = -0.073672032 x = -0.073672032 Simplifying x = -0.073672032Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.573672032, -0.073672032}
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