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Simplifying x = 26 + -12x + -1x2 Solving x = 26 + -12x + -1x2 Solving for variable 'x'. Reorder the terms: -26 + x + 12x + x2 = 26 + -12x + -1x2 + -26 + 12x + x2 Combine like terms: x + 12x = 13x -26 + 13x + x2 = 26 + -12x + -1x2 + -26 + 12x + x2 Reorder the terms: -26 + 13x + x2 = 26 + -26 + -12x + 12x + -1x2 + x2 Combine like terms: 26 + -26 = 0 -26 + 13x + x2 = 0 + -12x + 12x + -1x2 + x2 -26 + 13x + x2 = -12x + 12x + -1x2 + x2 Combine like terms: -12x + 12x = 0 -26 + 13x + x2 = 0 + -1x2 + x2 -26 + 13x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -26 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + 13x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + 13x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 13x + x2 = 0 + 26 13x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 13x + x2 = 26 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = 26 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 26 + 42.25 Combine like terms: 26 + 42.25 = 68.25 42.25 + 13x + x2 = 68.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 68.25 Calculate the square root of the right side: 8.261355821 Break this problem into two subproblems by setting (x + 6.5) equal to 8.261355821 and -8.261355821.Subproblem 1
x + 6.5 = 8.261355821 Simplifying x + 6.5 = 8.261355821 Reorder the terms: 6.5 + x = 8.261355821 Solving 6.5 + x = 8.261355821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 8.261355821 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 8.261355821 + -6.5 x = 8.261355821 + -6.5 Combine like terms: 8.261355821 + -6.5 = 1.761355821 x = 1.761355821 Simplifying x = 1.761355821Subproblem 2
x + 6.5 = -8.261355821 Simplifying x + 6.5 = -8.261355821 Reorder the terms: 6.5 + x = -8.261355821 Solving 6.5 + x = -8.261355821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -8.261355821 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -8.261355821 + -6.5 x = -8.261355821 + -6.5 Combine like terms: -8.261355821 + -6.5 = -14.761355821 x = -14.761355821 Simplifying x = -14.761355821Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.761355821, -14.761355821}
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