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Simplifying 0 = 12x2 + 24x + 24 Reorder the terms: 0 = 24 + 24x + 12x2 Solving 0 = 24 + 24x + 12x2 Solving for variable 'x'. Combine like terms: 0 + -24 = -24 -24 + -24x + -12x2 = 24 + 24x + 12x2 + -24 + -24x + -12x2 Reorder the terms: -24 + -24x + -12x2 = 24 + -24 + 24x + -24x + 12x2 + -12x2 Combine like terms: 24 + -24 = 0 -24 + -24x + -12x2 = 0 + 24x + -24x + 12x2 + -12x2 -24 + -24x + -12x2 = 24x + -24x + 12x2 + -12x2 Combine like terms: 24x + -24x = 0 -24 + -24x + -12x2 = 0 + 12x2 + -12x2 -24 + -24x + -12x2 = 12x2 + -12x2 Combine like terms: 12x2 + -12x2 = 0 -24 + -24x + -12x2 = 0 Factor out the Greatest Common Factor (GCF), '-12'. -12(2 + 2x + x2) = 0 Ignore the factor -12.Subproblem 1
Set the factor '(2 + 2x + x2)' equal to zero and attempt to solve: Simplifying 2 + 2x + x2 = 0 Solving 2 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 2x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 2x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 2x + x2 = 0 + -2 2x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 2x + x2 = -2 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 = -2 + 1 Reorder the terms: 1 + 2x + x2 = -2 + 1 Combine like terms: -2 + 1 = -1 1 + 2x + x2 = -1 Factor a perfect square on the left side: (x + 1)(x + 1) = -1 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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