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Simplifying 2x2 + -5x + 2 = (x + -3)(x + 2) + 3x Reorder the terms: 2 + -5x + 2x2 = (x + -3)(x + 2) + 3x Reorder the terms: 2 + -5x + 2x2 = (-3 + x)(x + 2) + 3x Reorder the terms: 2 + -5x + 2x2 = (-3 + x)(2 + x) + 3x Multiply (-3 + x) * (2 + x) 2 + -5x + 2x2 = (-3(2 + x) + x(2 + x)) + 3x 2 + -5x + 2x2 = ((2 * -3 + x * -3) + x(2 + x)) + 3x 2 + -5x + 2x2 = ((-6 + -3x) + x(2 + x)) + 3x 2 + -5x + 2x2 = (-6 + -3x + (2 * x + x * x)) + 3x 2 + -5x + 2x2 = (-6 + -3x + (2x + x2)) + 3x Combine like terms: -3x + 2x = -1x 2 + -5x + 2x2 = (-6 + -1x + x2) + 3x Reorder the terms: 2 + -5x + 2x2 = -6 + -1x + 3x + x2 Combine like terms: -1x + 3x = 2x 2 + -5x + 2x2 = -6 + 2x + x2 Solving 2 + -5x + 2x2 = -6 + 2x + x2 Solving for variable 'x'. Reorder the terms: 2 + 6 + -5x + -2x + 2x2 + -1x2 = -6 + 2x + x2 + 6 + -2x + -1x2 Combine like terms: 2 + 6 = 8 8 + -5x + -2x + 2x2 + -1x2 = -6 + 2x + x2 + 6 + -2x + -1x2 Combine like terms: -5x + -2x = -7x 8 + -7x + 2x2 + -1x2 = -6 + 2x + x2 + 6 + -2x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 8 + -7x + 1x2 = -6 + 2x + x2 + 6 + -2x + -1x2 Reorder the terms: 8 + -7x + 1x2 = -6 + 6 + 2x + -2x + x2 + -1x2 Combine like terms: -6 + 6 = 0 8 + -7x + 1x2 = 0 + 2x + -2x + x2 + -1x2 8 + -7x + 1x2 = 2x + -2x + x2 + -1x2 Combine like terms: 2x + -2x = 0 8 + -7x + 1x2 = 0 + x2 + -1x2 8 + -7x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 8 + -7x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -7x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -7x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -7x + x2 = 0 + -8 -7x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -7x + x2 = -8 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -8 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -8 + 12.25 Combine like terms: -8 + 12.25 = 4.25 12.25 + -7x + x2 = 4.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + -3.5) equal to 2.061552813 and -2.061552813.Subproblem 1
x + -3.5 = 2.061552813 Simplifying x + -3.5 = 2.061552813 Reorder the terms: -3.5 + x = 2.061552813 Solving -3.5 + x = 2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 2.061552813 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 2.061552813 + 3.5 x = 2.061552813 + 3.5 Combine like terms: 2.061552813 + 3.5 = 5.561552813 x = 5.561552813 Simplifying x = 5.561552813Subproblem 2
x + -3.5 = -2.061552813 Simplifying x + -3.5 = -2.061552813 Reorder the terms: -3.5 + x = -2.061552813 Solving -3.5 + x = -2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -2.061552813 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -2.061552813 + 3.5 x = -2.061552813 + 3.5 Combine like terms: -2.061552813 + 3.5 = 1.438447187 x = 1.438447187 Simplifying x = 1.438447187Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.561552813, 1.438447187}
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