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Simplifying (-1x2 + 4x + -6) + (2x2 + -5x + 1) = 0 Reorder the terms: (-6 + 4x + -1x2) + (2x2 + -5x + 1) = 0 Remove parenthesis around (-6 + 4x + -1x2) -6 + 4x + -1x2 + (2x2 + -5x + 1) = 0 Reorder the terms: -6 + 4x + -1x2 + (1 + -5x + 2x2) = 0 Remove parenthesis around (1 + -5x + 2x2) -6 + 4x + -1x2 + 1 + -5x + 2x2 = 0 Reorder the terms: -6 + 1 + 4x + -5x + -1x2 + 2x2 = 0 Combine like terms: -6 + 1 = -5 -5 + 4x + -5x + -1x2 + 2x2 = 0 Combine like terms: 4x + -5x = -1x -5 + -1x + -1x2 + 2x2 = 0 Combine like terms: -1x2 + 2x2 = 1x2 -5 + -1x + 1x2 = 0 Solving -5 + -1x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -1x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -1x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x + x2 = 0 + 5 -1x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -1x + x2 = 5 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 = 5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 5 + 0.25 Combine like terms: 5 + 0.25 = 5.25 0.25 + -1x + x2 = 5.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x + -0.5) equal to 2.291287847 and -2.291287847.Subproblem 1
x + -0.5 = 2.291287847 Simplifying x + -0.5 = 2.291287847 Reorder the terms: -0.5 + x = 2.291287847 Solving -0.5 + x = 2.291287847 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 = 2.291287847 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.291287847 + 0.5 x = 2.291287847 + 0.5 Combine like terms: 2.291287847 + 0.5 = 2.791287847 x = 2.791287847 Simplifying x = 2.791287847Subproblem 2
x + -0.5 = -2.291287847 Simplifying x + -0.5 = -2.291287847 Reorder the terms: -0.5 + x = -2.291287847 Solving -0.5 + x = -2.291287847 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 = -2.291287847 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.291287847 + 0.5 x = -2.291287847 + 0.5 Combine like terms: -2.291287847 + 0.5 = -1.791287847 x = -1.791287847 Simplifying x = -1.791287847Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.791287847, -1.791287847}
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