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Simplifying 4x + -1(x2 + 2x) + 3(3x2 + -6x + 4) = 0 Reorder the terms: 4x + -1(2x + x2) + 3(3x2 + -6x + 4) = 0 4x + (2x * -1 + x2 * -1) + 3(3x2 + -6x + 4) = 0 4x + (-2x + -1x2) + 3(3x2 + -6x + 4) = 0 Reorder the terms: 4x + -2x + -1x2 + 3(4 + -6x + 3x2) = 0 4x + -2x + -1x2 + (4 * 3 + -6x * 3 + 3x2 * 3) = 0 4x + -2x + -1x2 + (12 + -18x + 9x2) = 0 Reorder the terms: 12 + 4x + -2x + -18x + -1x2 + 9x2 = 0 Combine like terms: 4x + -2x = 2x 12 + 2x + -18x + -1x2 + 9x2 = 0 Combine like terms: 2x + -18x = -16x 12 + -16x + -1x2 + 9x2 = 0 Combine like terms: -1x2 + 9x2 = 8x2 12 + -16x + 8x2 = 0 Solving 12 + -16x + 8x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(3 + -4x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + -4x + 2x2)' equal to zero and attempt to solve: Simplifying 3 + -4x + 2x2 = 0 Solving 3 + -4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + -2x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -2x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -2x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -2x + x2 = 0 + -1.5 -2x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -2x + x2 = -1.5 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 = -1.5 + 1 Reorder the terms: 1 + -2x + x2 = -1.5 + 1 Combine like terms: -1.5 + 1 = -0.5 1 + -2x + x2 = -0.5 Factor a perfect square on the left side: (x + -1)(x + -1) = -0.5 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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