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Simplifying 3x(5 + -2x) = 6x(x + 2) + 81 (5 * 3x + -2x * 3x) = 6x(x + 2) + 81 (15x + -6x2) = 6x(x + 2) + 81 Reorder the terms: 15x + -6x2 = 6x(2 + x) + 81 15x + -6x2 = (2 * 6x + x * 6x) + 81 15x + -6x2 = (12x + 6x2) + 81 Reorder the terms: 15x + -6x2 = 81 + 12x + 6x2 Solving 15x + -6x2 = 81 + 12x + 6x2 Solving for variable 'x'. Reorder the terms: -81 + 15x + -12x + -6x2 + -6x2 = 81 + 12x + 6x2 + -81 + -12x + -6x2 Combine like terms: 15x + -12x = 3x -81 + 3x + -6x2 + -6x2 = 81 + 12x + 6x2 + -81 + -12x + -6x2 Combine like terms: -6x2 + -6x2 = -12x2 -81 + 3x + -12x2 = 81 + 12x + 6x2 + -81 + -12x + -6x2 Reorder the terms: -81 + 3x + -12x2 = 81 + -81 + 12x + -12x + 6x2 + -6x2 Combine like terms: 81 + -81 = 0 -81 + 3x + -12x2 = 0 + 12x + -12x + 6x2 + -6x2 -81 + 3x + -12x2 = 12x + -12x + 6x2 + -6x2 Combine like terms: 12x + -12x = 0 -81 + 3x + -12x2 = 0 + 6x2 + -6x2 -81 + 3x + -12x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -81 + 3x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-27 + x + -4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-27 + x + -4x2)' equal to zero and attempt to solve: Simplifying -27 + x + -4x2 = 0 Solving -27 + x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 6.75 + -0.25x + x2 = 0 Move the constant term to the right: Add '-6.75' to each side of the equation. 6.75 + -0.25x + -6.75 + x2 = 0 + -6.75 Reorder the terms: 6.75 + -6.75 + -0.25x + x2 = 0 + -6.75 Combine like terms: 6.75 + -6.75 = 0.00 0.00 + -0.25x + x2 = 0 + -6.75 -0.25x + x2 = 0 + -6.75 Combine like terms: 0 + -6.75 = -6.75 -0.25x + x2 = -6.75 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 = -6.75 + 0.25 Reorder the terms: 0.25 + -0.25x + x2 = -6.75 + 0.25 Combine like terms: -6.75 + 0.25 = -6.5 0.25 + -0.25x + x2 = -6.5 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -6.5 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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