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Simplifying 2x(x + 1) = 6(x + -4) Reorder the terms: 2x(1 + x) = 6(x + -4) (1 * 2x + x * 2x) = 6(x + -4) (2x + 2x2) = 6(x + -4) Reorder the terms: 2x + 2x2 = 6(-4 + x) 2x + 2x2 = (-4 * 6 + x * 6) 2x + 2x2 = (-24 + 6x) Solving 2x + 2x2 = -24 + 6x Solving for variable 'x'. Reorder the terms: 24 + 2x + -6x + 2x2 = -24 + 6x + 24 + -6x Combine like terms: 2x + -6x = -4x 24 + -4x + 2x2 = -24 + 6x + 24 + -6x Reorder the terms: 24 + -4x + 2x2 = -24 + 24 + 6x + -6x Combine like terms: -24 + 24 = 0 24 + -4x + 2x2 = 0 + 6x + -6x 24 + -4x + 2x2 = 6x + -6x Combine like terms: 6x + -6x = 0 24 + -4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(12 + -2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + -2x + x2)' equal to zero and attempt to solve: Simplifying 12 + -2x + x2 = 0 Solving 12 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -2x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -2x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -2x + x2 = 0 + -12 -2x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -2x + x2 = -12 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -12 + 1 Reorder the terms: 1 + -2x + x2 = -12 + 1 Combine like terms: -12 + 1 = -11 1 + -2x + x2 = -11 Factor a perfect square on the left side: (x + -1)(x + -1) = -11 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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