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Simplifying 2x(4x + -3) = 8x * 2 + -18 Reorder the terms: 2x(-3 + 4x) = 8x * 2 + -18 (-3 * 2x + 4x * 2x) = 8x * 2 + -18 (-6x + 8x2) = 8x * 2 + -18 Reorder the terms for easier multiplication: -6x + 8x2 = 8 * 2x + -18 Multiply 8 * 2 -6x + 8x2 = 16x + -18 Reorder the terms: -6x + 8x2 = -18 + 16x Solving -6x + 8x2 = -18 + 16x Solving for variable 'x'. Reorder the terms: 18 + -6x + -16x + 8x2 = -18 + 16x + 18 + -16x Combine like terms: -6x + -16x = -22x 18 + -22x + 8x2 = -18 + 16x + 18 + -16x Reorder the terms: 18 + -22x + 8x2 = -18 + 18 + 16x + -16x Combine like terms: -18 + 18 = 0 18 + -22x + 8x2 = 0 + 16x + -16x 18 + -22x + 8x2 = 16x + -16x Combine like terms: 16x + -16x = 0 18 + -22x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(9 + -11x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -11x + 4x2)' equal to zero and attempt to solve: Simplifying 9 + -11x + 4x2 = 0 Solving 9 + -11x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + -2.75x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -2.75x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -2.75x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -2.75x + x2 = 0 + -2.25 -2.75x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -2.75x + x2 = -2.25 The x term is -2.75x. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75x + 1.890625 + x2 = -2.25 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = -2.25 + 1.890625 Combine like terms: -2.25 + 1.890625 = -0.359375 1.890625 + -2.75x + x2 = -0.359375 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = -0.359375 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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