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Simplifying 4x + 2x(x + 3) = 6(x + -1) Reorder the terms: 4x + 2x(3 + x) = 6(x + -1) 4x + (3 * 2x + x * 2x) = 6(x + -1) 4x + (6x + 2x2) = 6(x + -1) Combine like terms: 4x + 6x = 10x 10x + 2x2 = 6(x + -1) Reorder the terms: 10x + 2x2 = 6(-1 + x) 10x + 2x2 = (-1 * 6 + x * 6) 10x + 2x2 = (-6 + 6x) Solving 10x + 2x2 = -6 + 6x Solving for variable 'x'. Reorder the terms: 6 + 10x + -6x + 2x2 = -6 + 6x + 6 + -6x Combine like terms: 10x + -6x = 4x 6 + 4x + 2x2 = -6 + 6x + 6 + -6x Reorder the terms: 6 + 4x + 2x2 = -6 + 6 + 6x + -6x Combine like terms: -6 + 6 = 0 6 + 4x + 2x2 = 0 + 6x + -6x 6 + 4x + 2x2 = 6x + -6x Combine like terms: 6x + -6x = 0 6 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + 2x + x2)' equal to zero and attempt to solve: Simplifying 3 + 2x + x2 = 0 Solving 3 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 2x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 2x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2x + x2 = 0 + -3 2x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 2x + x2 = -3 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 = -3 + 1 Reorder the terms: 1 + 2x + x2 = -3 + 1 Combine like terms: -3 + 1 = -2 1 + 2x + x2 = -2 Factor a perfect square on the left side: (x + 1)(x + 1) = -2 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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