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Simplifying 0 = 6x2 + 48x + 120 Reorder the terms: 0 = 120 + 48x + 6x2 Solving 0 = 120 + 48x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -120 = -120 -120 + -48x + -6x2 = 120 + 48x + 6x2 + -120 + -48x + -6x2 Reorder the terms: -120 + -48x + -6x2 = 120 + -120 + 48x + -48x + 6x2 + -6x2 Combine like terms: 120 + -120 = 0 -120 + -48x + -6x2 = 0 + 48x + -48x + 6x2 + -6x2 -120 + -48x + -6x2 = 48x + -48x + 6x2 + -6x2 Combine like terms: 48x + -48x = 0 -120 + -48x + -6x2 = 0 + 6x2 + -6x2 -120 + -48x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -120 + -48x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-6'. -6(20 + 8x + x2) = 0 Ignore the factor -6.Subproblem 1
Set the factor '(20 + 8x + x2)' equal to zero and attempt to solve: Simplifying 20 + 8x + x2 = 0 Solving 20 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + 8x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + 8x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + 8x + x2 = 0 + -20 8x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 8x + x2 = -20 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -20 + 16 Reorder the terms: 16 + 8x + x2 = -20 + 16 Combine like terms: -20 + 16 = -4 16 + 8x + x2 = -4 Factor a perfect square on the left side: (x + 4)(x + 4) = -4 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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