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Simplifying (x + 2)(x + 2)(x + 2) = x3 + 2x Reorder the terms: (2 + x)(x + 2)(x + 2) = x3 + 2x Reorder the terms: (2 + x)(2 + x)(x + 2) = x3 + 2x Reorder the terms: (2 + x)(2 + x)(2 + x) = x3 + 2x Multiply (2 + x) * (2 + x) (2(2 + x) + x(2 + x))(2 + x) = x3 + 2x ((2 * 2 + x * 2) + x(2 + x))(2 + x) = x3 + 2x ((4 + 2x) + x(2 + x))(2 + x) = x3 + 2x (4 + 2x + (2 * x + x * x))(2 + x) = x3 + 2x (4 + 2x + (2x + x2))(2 + x) = x3 + 2x Combine like terms: 2x + 2x = 4x (4 + 4x + x2)(2 + x) = x3 + 2x Multiply (4 + 4x + x2) * (2 + x) (4(2 + x) + 4x * (2 + x) + x2(2 + x)) = x3 + 2x ((2 * 4 + x * 4) + 4x * (2 + x) + x2(2 + x)) = x3 + 2x ((8 + 4x) + 4x * (2 + x) + x2(2 + x)) = x3 + 2x (8 + 4x + (2 * 4x + x * 4x) + x2(2 + x)) = x3 + 2x (8 + 4x + (8x + 4x2) + x2(2 + x)) = x3 + 2x (8 + 4x + 8x + 4x2 + (2 * x2 + x * x2)) = x3 + 2x (8 + 4x + 8x + 4x2 + (2x2 + x3)) = x3 + 2x Combine like terms: 4x + 8x = 12x (8 + 12x + 4x2 + 2x2 + x3) = x3 + 2x Combine like terms: 4x2 + 2x2 = 6x2 (8 + 12x + 6x2 + x3) = x3 + 2x Reorder the terms: 8 + 12x + 6x2 + x3 = 2x + x3 Add '-1x3' to each side of the equation. 8 + 12x + 6x2 + x3 + -1x3 = 2x + x3 + -1x3 Combine like terms: x3 + -1x3 = 0 8 + 12x + 6x2 + 0 = 2x + x3 + -1x3 8 + 12x + 6x2 = 2x + x3 + -1x3 Combine like terms: x3 + -1x3 = 0 8 + 12x + 6x2 = 2x + 0 8 + 12x + 6x2 = 2x Solving 8 + 12x + 6x2 = 2x Solving for variable 'x'. Reorder the terms: 8 + 12x + -2x + 6x2 = 2x + -2x Combine like terms: 12x + -2x = 10x 8 + 10x + 6x2 = 2x + -2x Combine like terms: 2x + -2x = 0 8 + 10x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 5x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + 5x + 3x2)' equal to zero and attempt to solve: Simplifying 4 + 5x + 3x2 = 0 Solving 4 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 1.666666667x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 1.666666667x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 1.666666667x + x2 = 0 + -1.333333333 1.666666667x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 1.666666667x + x2 = -1.333333333 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 = -1.333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = -1.333333333 + 0.6944444447 Combine like terms: -1.333333333 + 0.6944444447 = -0.6388888883 0.6944444447 + 1.666666667x + x2 = -0.6388888883 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = -0.6388888883 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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