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Simplifying 4x2 + -6x = -4 Reorder the terms: -6x + 4x2 = -4 Solving -6x + 4x2 = -4 Solving for variable 'x'. Reorder the terms: 4 + -6x + 4x2 = -4 + 4 Combine like terms: -4 + 4 = 0 4 + -6x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -3x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -3x + 2x2)' equal to zero and attempt to solve: Simplifying 2 + -3x + 2x2 = 0 Solving 2 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1 + -1.5x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -1.5x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -1.5x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1.5x + x2 = 0 + -1 -1.5x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -1.5x + x2 = -1 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = -1 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -1 + 0.5625 Combine like terms: -1 + 0.5625 = -0.4375 0.5625 + -1.5x + x2 = -0.4375 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = -0.4375 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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