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Simplifying 4x + -1 = 2x2 + 3 Reorder the terms: -1 + 4x = 2x2 + 3 Reorder the terms: -1 + 4x = 3 + 2x2 Solving -1 + 4x = 3 + 2x2 Solving for variable 'x'. Reorder the terms: -1 + -3 + 4x + -2x2 = 3 + 2x2 + -3 + -2x2 Combine like terms: -1 + -3 = -4 -4 + 4x + -2x2 = 3 + 2x2 + -3 + -2x2 Reorder the terms: -4 + 4x + -2x2 = 3 + -3 + 2x2 + -2x2 Combine like terms: 3 + -3 = 0 -4 + 4x + -2x2 = 0 + 2x2 + -2x2 -4 + 4x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -4 + 4x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + 2x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-2 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying -2 + 2x + -1x2 = 0 Solving -2 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -2x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -2x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -2x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2x + x2 = 0 + -2 -2x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -2x + x2 = -2 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -2 + 1 Reorder the terms: 1 + -2x + x2 = -2 + 1 Combine like terms: -2 + 1 = -1 1 + -2x + x2 = -1 Factor a perfect square on the left side: (x + -1)(x + -1) = -1 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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