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Simplifying -6x(x + 1) = 24 Reorder the terms: -6x(1 + x) = 24 (1 * -6x + x * -6x) = 24 (-6x + -6x2) = 24 Solving -6x + -6x2 = 24 Solving for variable 'x'. Reorder the terms: -24 + -6x + -6x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + -6x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-6'. -6(4 + x + x2) = 0 Ignore the factor -6.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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