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Simplifying 2x(4x + 3) = 4x + -18 Reorder the terms: 2x(3 + 4x) = 4x + -18 (3 * 2x + 4x * 2x) = 4x + -18 (6x + 8x2) = 4x + -18 Reorder the terms: 6x + 8x2 = -18 + 4x Solving 6x + 8x2 = -18 + 4x Solving for variable 'x'. Reorder the terms: 18 + 6x + -4x + 8x2 = -18 + 4x + 18 + -4x Combine like terms: 6x + -4x = 2x 18 + 2x + 8x2 = -18 + 4x + 18 + -4x Reorder the terms: 18 + 2x + 8x2 = -18 + 18 + 4x + -4x Combine like terms: -18 + 18 = 0 18 + 2x + 8x2 = 0 + 4x + -4x 18 + 2x + 8x2 = 4x + -4x Combine like terms: 4x + -4x = 0 18 + 2x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(9 + x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + x + 4x2)' equal to zero and attempt to solve: Simplifying 9 + x + 4x2 = 0 Solving 9 + x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + 0.25x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + 0.25x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + 0.25x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + 0.25x + x2 = 0 + -2.25 0.25x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 0.25x + x2 = -2.25 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.25x + 0.25 + x2 = -2.25 + 0.25 Reorder the terms: 0.25 + 0.25x + x2 = -2.25 + 0.25 Combine like terms: -2.25 + 0.25 = -2 0.25 + 0.25x + x2 = -2 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -2 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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