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Simplifying 4x + 12 = 16x(4 + -4x) + -12 Reorder the terms: 12 + 4x = 16x(4 + -4x) + -12 12 + 4x = (4 * 16x + -4x * 16x) + -12 12 + 4x = (64x + -64x2) + -12 Reorder the terms: 12 + 4x = -12 + 64x + -64x2 Solving 12 + 4x = -12 + 64x + -64x2 Solving for variable 'x'. Reorder the terms: 12 + 12 + 4x + -64x + 64x2 = -12 + 64x + -64x2 + 12 + -64x + 64x2 Combine like terms: 12 + 12 = 24 24 + 4x + -64x + 64x2 = -12 + 64x + -64x2 + 12 + -64x + 64x2 Combine like terms: 4x + -64x = -60x 24 + -60x + 64x2 = -12 + 64x + -64x2 + 12 + -64x + 64x2 Reorder the terms: 24 + -60x + 64x2 = -12 + 12 + 64x + -64x + -64x2 + 64x2 Combine like terms: -12 + 12 = 0 24 + -60x + 64x2 = 0 + 64x + -64x + -64x2 + 64x2 24 + -60x + 64x2 = 64x + -64x + -64x2 + 64x2 Combine like terms: 64x + -64x = 0 24 + -60x + 64x2 = 0 + -64x2 + 64x2 24 + -60x + 64x2 = -64x2 + 64x2 Combine like terms: -64x2 + 64x2 = 0 24 + -60x + 64x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(6 + -15x + 16x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(6 + -15x + 16x2)' equal to zero and attempt to solve: Simplifying 6 + -15x + 16x2 = 0 Solving 6 + -15x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.375 + -0.9375x + x2 = 0 Move the constant term to the right: Add '-0.375' to each side of the equation. 0.375 + -0.9375x + -0.375 + x2 = 0 + -0.375 Reorder the terms: 0.375 + -0.375 + -0.9375x + x2 = 0 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + -0.9375x + x2 = 0 + -0.375 -0.9375x + x2 = 0 + -0.375 Combine like terms: 0 + -0.375 = -0.375 -0.9375x + x2 = -0.375 The x term is -0.9375x. Take half its coefficient (-0.46875). Square it (0.2197265625) and add it to both sides. Add '0.2197265625' to each side of the equation. -0.9375x + 0.2197265625 + x2 = -0.375 + 0.2197265625 Reorder the terms: 0.2197265625 + -0.9375x + x2 = -0.375 + 0.2197265625 Combine like terms: -0.375 + 0.2197265625 = -0.1552734375 0.2197265625 + -0.9375x + x2 = -0.1552734375 Factor a perfect square on the left side: (x + -0.46875)(x + -0.46875) = -0.1552734375 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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