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Simplifying 3x(x + 4) + -7x = 2(x + -6) Reorder the terms: 3x(4 + x) + -7x = 2(x + -6) (4 * 3x + x * 3x) + -7x = 2(x + -6) (12x + 3x2) + -7x = 2(x + -6) Reorder the terms: 12x + -7x + 3x2 = 2(x + -6) Combine like terms: 12x + -7x = 5x 5x + 3x2 = 2(x + -6) Reorder the terms: 5x + 3x2 = 2(-6 + x) 5x + 3x2 = (-6 * 2 + x * 2) 5x + 3x2 = (-12 + 2x) Solving 5x + 3x2 = -12 + 2x Solving for variable 'x'. Reorder the terms: 12 + 5x + -2x + 3x2 = -12 + 2x + 12 + -2x Combine like terms: 5x + -2x = 3x 12 + 3x + 3x2 = -12 + 2x + 12 + -2x Reorder the terms: 12 + 3x + 3x2 = -12 + 12 + 2x + -2x Combine like terms: -12 + 12 = 0 12 + 3x + 3x2 = 0 + 2x + -2x 12 + 3x + 3x2 = 2x + -2x Combine like terms: 2x + -2x = 0 12 + 3x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(4 + x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + x + x2)' equal to zero and attempt to solve: Simplifying 4 + x + x2 = 0 Solving 4 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x + x2 = 0 + -4 x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 x + x2 = -4 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 = -4 + 0.25 Reorder the terms: 0.25 + x + x2 = -4 + 0.25 Combine like terms: -4 + 0.25 = -3.75 0.25 + x + x2 = -3.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -3.75 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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