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Simplifying 2x2 + x + -27 + -1x2 + -1x + -1x + 1 = 0 Reorder the terms: -27 + 1 + x + -1x + -1x + 2x2 + -1x2 = 0 Combine like terms: -27 + 1 = -26 -26 + x + -1x + -1x + 2x2 + -1x2 = 0 Combine like terms: x + -1x = 0 -26 + 0 + -1x + 2x2 + -1x2 = 0 -26 + -1x + 2x2 + -1x2 = 0 Combine like terms: 2x2 + -1x2 = 1x2 -26 + -1x + 1x2 = 0 Solving -26 + -1x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + -1x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + -1x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -1x + x2 = 0 + 26 -1x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 -1x + x2 = 26 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 26 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 26 + 0.25 Combine like terms: 26 + 0.25 = 26.25 0.25 + -1x + x2 = 26.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (x + -0.5) equal to 5.123475383 and -5.123475383.Subproblem 1
x + -0.5 = 5.123475383 Simplifying x + -0.5 = 5.123475383 Reorder the terms: -0.5 + x = 5.123475383 Solving -0.5 + x = 5.123475383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 5.123475383 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 5.123475383 + 0.5 x = 5.123475383 + 0.5 Combine like terms: 5.123475383 + 0.5 = 5.623475383 x = 5.623475383 Simplifying x = 5.623475383Subproblem 2
x + -0.5 = -5.123475383 Simplifying x + -0.5 = -5.123475383 Reorder the terms: -0.5 + x = -5.123475383 Solving -0.5 + x = -5.123475383 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -5.123475383 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -5.123475383 + 0.5 x = -5.123475383 + 0.5 Combine like terms: -5.123475383 + 0.5 = -4.623475383 x = -4.623475383 Simplifying x = -4.623475383Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.623475383, -4.623475383}
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