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Simplifying -2x(x + 3) = 6 Reorder the terms: -2x(3 + x) = 6 (3 * -2x + x * -2x) = 6 (-6x + -2x2) = 6 Solving -6x + -2x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + -6x + -2x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + -6x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(3 + 3x + x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(3 + 3x + x2)' equal to zero and attempt to solve: Simplifying 3 + 3x + x2 = 0 Solving 3 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 3x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 3x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 3x + x2 = 0 + -3 3x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 3x + x2 = -3 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 = -3 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -3 + 2.25 Combine like terms: -3 + 2.25 = -0.75 2.25 + 3x + x2 = -0.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -0.75 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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