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Simplifying 6 + -3x(1 + -1x) = -42 + -6x 6 + (1 * -3x + -1x * -3x) = -42 + -6x 6 + (-3x + 3x2) = -42 + -6x Solving 6 + -3x + 3x2 = -42 + -6x Solving for variable 'x'. Reorder the terms: 6 + 42 + -3x + 6x + 3x2 = -42 + -6x + 42 + 6x Combine like terms: 6 + 42 = 48 48 + -3x + 6x + 3x2 = -42 + -6x + 42 + 6x Combine like terms: -3x + 6x = 3x 48 + 3x + 3x2 = -42 + -6x + 42 + 6x Reorder the terms: 48 + 3x + 3x2 = -42 + 42 + -6x + 6x Combine like terms: -42 + 42 = 0 48 + 3x + 3x2 = 0 + -6x + 6x 48 + 3x + 3x2 = -6x + 6x Combine like terms: -6x + 6x = 0 48 + 3x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(16 + x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(16 + x + x2)' equal to zero and attempt to solve: Simplifying 16 + x + x2 = 0 Solving 16 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + x + x2 = 0 + -16 x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 x + x2 = -16 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. x + 0.25 + x2 = -16 + 0.25 Reorder the terms: 0.25 + x + x2 = -16 + 0.25 Combine like terms: -16 + 0.25 = -15.75 0.25 + x + x2 = -15.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -15.75 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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