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Simplifying (2x2 + 4x + -2) + -1(5x2 + 6x + 3) + (-2x2 + -3x + -5) = 0 Reorder the terms: (-2 + 4x + 2x2) + -1(5x2 + 6x + 3) + (-2x2 + -3x + -5) = 0 Remove parenthesis around (-2 + 4x + 2x2) -2 + 4x + 2x2 + -1(5x2 + 6x + 3) + (-2x2 + -3x + -5) = 0 Reorder the terms: -2 + 4x + 2x2 + -1(3 + 6x + 5x2) + (-2x2 + -3x + -5) = 0 -2 + 4x + 2x2 + (3 * -1 + 6x * -1 + 5x2 * -1) + (-2x2 + -3x + -5) = 0 -2 + 4x + 2x2 + (-3 + -6x + -5x2) + (-2x2 + -3x + -5) = 0 Reorder the terms: -2 + 4x + 2x2 + -3 + -6x + -5x2 + (-5 + -3x + -2x2) = 0 Remove parenthesis around (-5 + -3x + -2x2) -2 + 4x + 2x2 + -3 + -6x + -5x2 + -5 + -3x + -2x2 = 0 Reorder the terms: -2 + -3 + -5 + 4x + -6x + -3x + 2x2 + -5x2 + -2x2 = 0 Combine like terms: -2 + -3 = -5 -5 + -5 + 4x + -6x + -3x + 2x2 + -5x2 + -2x2 = 0 Combine like terms: -5 + -5 = -10 -10 + 4x + -6x + -3x + 2x2 + -5x2 + -2x2 = 0 Combine like terms: 4x + -6x = -2x -10 + -2x + -3x + 2x2 + -5x2 + -2x2 = 0 Combine like terms: -2x + -3x = -5x -10 + -5x + 2x2 + -5x2 + -2x2 = 0 Combine like terms: 2x2 + -5x2 = -3x2 -10 + -5x + -3x2 + -2x2 = 0 Combine like terms: -3x2 + -2x2 = -5x2 -10 + -5x + -5x2 = 0 Solving -10 + -5x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-5'. -5(2 + x + x2) = 0 Ignore the factor -5.Subproblem 1
Set the factor '(2 + x + x2)' equal to zero and attempt to solve: Simplifying 2 + x + x2 = 0 Solving 2 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x + x2 = 0 + -2 x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 x + x2 = -2 The x term is x. 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. x + 0.25 + x2 = -2 + 0.25 Reorder the terms: 0.25 + x + x2 = -2 + 0.25 Combine like terms: -2 + 0.25 = -1.75 0.25 + x + x2 = -1.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -1.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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