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Simplifying 6x(3x + 9) = -72 Reorder the terms: 6x(9 + 3x) = -72 (9 * 6x + 3x * 6x) = -72 (54x + 18x2) = -72 Solving 54x + 18x2 = -72 Solving for variable 'x'. Reorder the terms: 72 + 54x + 18x2 = -72 + 72 Combine like terms: -72 + 72 = 0 72 + 54x + 18x2 = 0 Factor out the Greatest Common Factor (GCF), '18'. 18(4 + 3x + x2) = 0 Ignore the factor 18.Subproblem 1
Set the factor '(4 + 3x + x2)' equal to zero and attempt to solve: Simplifying 4 + 3x + x2 = 0 Solving 4 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 3x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 3x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3x + x2 = 0 + -4 3x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 3x + x2 = -4 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -4 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -4 + 2.25 Combine like terms: -4 + 2.25 = -1.75 2.25 + 3x + x2 = -1.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -1.75 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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