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Simplifying 4x(x + 2) = 2(x + -3) Reorder the terms: 4x(2 + x) = 2(x + -3) (2 * 4x + x * 4x) = 2(x + -3) (8x + 4x2) = 2(x + -3) Reorder the terms: 8x + 4x2 = 2(-3 + x) 8x + 4x2 = (-3 * 2 + x * 2) 8x + 4x2 = (-6 + 2x) Solving 8x + 4x2 = -6 + 2x Solving for variable 'x'. Reorder the terms: 6 + 8x + -2x + 4x2 = -6 + 2x + 6 + -2x Combine like terms: 8x + -2x = 6x 6 + 6x + 4x2 = -6 + 2x + 6 + -2x Reorder the terms: 6 + 6x + 4x2 = -6 + 6 + 2x + -2x Combine like terms: -6 + 6 = 0 6 + 6x + 4x2 = 0 + 2x + -2x 6 + 6x + 4x2 = 2x + -2x Combine like terms: 2x + -2x = 0 6 + 6x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 3x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying 3 + 3x + 2x2 = 0 Solving 3 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + 1.5x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + 1.5x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + 1.5x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + 1.5x + x2 = 0 + -1.5 1.5x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 1.5x + x2 = -1.5 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 = -1.5 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -1.5 + 0.5625 Combine like terms: -1.5 + 0.5625 = -0.9375 0.5625 + 1.5x + x2 = -0.9375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -0.9375 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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