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Simplifying -3x(x + 2) = 16 + -1x Reorder the terms: -3x(2 + x) = 16 + -1x (2 * -3x + x * -3x) = 16 + -1x (-6x + -3x2) = 16 + -1x Solving -6x + -3x2 = 16 + -1x Solving for variable 'x'. Reorder the terms: -16 + -6x + x + -3x2 = 16 + -1x + -16 + x Combine like terms: -6x + x = -5x -16 + -5x + -3x2 = 16 + -1x + -16 + x Reorder the terms: -16 + -5x + -3x2 = 16 + -16 + -1x + x Combine like terms: 16 + -16 = 0 -16 + -5x + -3x2 = 0 + -1x + x -16 + -5x + -3x2 = -1x + x Combine like terms: -1x + x = 0 -16 + -5x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(16 + 5x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(16 + 5x + 3x2)' equal to zero and attempt to solve: Simplifying 16 + 5x + 3x2 = 0 Solving 16 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 5.333333333 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '-5.333333333' to each side of the equation. 5.333333333 + 1.666666667x + -5.333333333 + x2 = 0 + -5.333333333 Reorder the terms: 5.333333333 + -5.333333333 + 1.666666667x + x2 = 0 + -5.333333333 Combine like terms: 5.333333333 + -5.333333333 = 0.000000000 0.000000000 + 1.666666667x + x2 = 0 + -5.333333333 1.666666667x + x2 = 0 + -5.333333333 Combine like terms: 0 + -5.333333333 = -5.333333333 1.666666667x + x2 = -5.333333333 The x term is 1.666666667x. Take half its coefficient (0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. 1.666666667x + 0.6944444447 + x2 = -5.333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = -5.333333333 + 0.6944444447 Combine like terms: -5.333333333 + 0.6944444447 = -4.6388888883 0.6944444447 + 1.666666667x + x2 = -4.6388888883 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = -4.6388888883 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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