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Simplifying 4x + 4(-1x2 + 3x) = 4 + -4x + 18x Reorder the terms: 4x + 4(3x + -1x2) = 4 + -4x + 18x 4x + (3x * 4 + -1x2 * 4) = 4 + -4x + 18x 4x + (12x + -4x2) = 4 + -4x + 18x Combine like terms: 4x + 12x = 16x 16x + -4x2 = 4 + -4x + 18x Combine like terms: -4x + 18x = 14x 16x + -4x2 = 4 + 14x Solving 16x + -4x2 = 4 + 14x Solving for variable 'x'. Reorder the terms: -4 + 16x + -14x + -4x2 = 4 + 14x + -4 + -14x Combine like terms: 16x + -14x = 2x -4 + 2x + -4x2 = 4 + 14x + -4 + -14x Reorder the terms: -4 + 2x + -4x2 = 4 + -4 + 14x + -14x Combine like terms: 4 + -4 = 0 -4 + 2x + -4x2 = 0 + 14x + -14x -4 + 2x + -4x2 = 14x + -14x Combine like terms: 14x + -14x = 0 -4 + 2x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + x + -2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + x + -2x2)' equal to zero and attempt to solve: Simplifying -2 + x + -2x2 = 0 Solving -2 + x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 1 + -0.5x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -0.5x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -0.5x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -0.5x + x2 = 0 + -1 -0.5x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -0.5x + x2 = -1 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. -0.5x + 0.25 + x2 = -1 + 0.25 Reorder the terms: 0.25 + -0.5x + x2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + -0.5x + x2 = -0.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.75 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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