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Simplifying 2x(4x + -3) = 8 * 2 + -18 Reorder the terms: 2x(-3 + 4x) = 8 * 2 + -18 (-3 * 2x + 4x * 2x) = 8 * 2 + -18 (-6x + 8x2) = 8 * 2 + -18 Multiply 8 * 2 -6x + 8x2 = 16 + -18 Combine like terms: 16 + -18 = -2 -6x + 8x2 = -2 Solving -6x + 8x2 = -2 Solving for variable 'x'. Reorder the terms: 2 + -6x + 8x2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + -6x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(1 + -3x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + -3x + 4x2)' equal to zero and attempt to solve: Simplifying 1 + -3x + 4x2 = 0 Solving 1 + -3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + -0.75x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -0.75x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -0.75x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -0.75x + x2 = 0 + -0.25 -0.75x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -0.75x + x2 = -0.25 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = -0.25 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = -0.25 + 0.140625 Combine like terms: -0.25 + 0.140625 = -0.109375 0.140625 + -0.75x + x2 = -0.109375 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = -0.109375 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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