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Simplifying 4(2x + -1) + -6x(3x + 1) = 4 + -6x Reorder the terms: 4(-1 + 2x) + -6x(3x + 1) = 4 + -6x (-1 * 4 + 2x * 4) + -6x(3x + 1) = 4 + -6x (-4 + 8x) + -6x(3x + 1) = 4 + -6x Reorder the terms: -4 + 8x + -6x(1 + 3x) = 4 + -6x -4 + 8x + (1 * -6x + 3x * -6x) = 4 + -6x -4 + 8x + (-6x + -18x2) = 4 + -6x Combine like terms: 8x + -6x = 2x -4 + 2x + -18x2 = 4 + -6x Solving -4 + 2x + -18x2 = 4 + -6x Solving for variable 'x'. Reorder the terms: -4 + -4 + 2x + 6x + -18x2 = 4 + -6x + -4 + 6x Combine like terms: -4 + -4 = -8 -8 + 2x + 6x + -18x2 = 4 + -6x + -4 + 6x Combine like terms: 2x + 6x = 8x -8 + 8x + -18x2 = 4 + -6x + -4 + 6x Reorder the terms: -8 + 8x + -18x2 = 4 + -4 + -6x + 6x Combine like terms: 4 + -4 = 0 -8 + 8x + -18x2 = 0 + -6x + 6x -8 + 8x + -18x2 = -6x + 6x Combine like terms: -6x + 6x = 0 -8 + 8x + -18x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 4x + -9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + 4x + -9x2)' equal to zero and attempt to solve: Simplifying -4 + 4x + -9x2 = 0 Solving -4 + 4x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 0.4444444444 + -0.4444444444x + x2 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + -0.4444444444x + -0.4444444444 + x2 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + -0.4444444444x + x2 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + -0.4444444444x + x2 = 0 + -0.4444444444 -0.4444444444x + x2 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 -0.4444444444x + x2 = -0.4444444444 The x term is -0.4444444444x. Take half its coefficient (-0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. -0.4444444444x + 0.04938271604 + x2 = -0.4444444444 + 0.04938271604 Reorder the terms: 0.04938271604 + -0.4444444444x + x2 = -0.4444444444 + 0.04938271604 Combine like terms: -0.4444444444 + 0.04938271604 = -0.39506172836 0.04938271604 + -0.4444444444x + x2 = -0.39506172836 Factor a perfect square on the left side: (x + -0.2222222222)(x + -0.2222222222) = -0.39506172836 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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