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Simplifying -4x(x + 2) + 2 = 2(x + 6) Reorder the terms: -4x(2 + x) + 2 = 2(x + 6) (2 * -4x + x * -4x) + 2 = 2(x + 6) (-8x + -4x2) + 2 = 2(x + 6) Reorder the terms: 2 + -8x + -4x2 = 2(x + 6) Reorder the terms: 2 + -8x + -4x2 = 2(6 + x) 2 + -8x + -4x2 = (6 * 2 + x * 2) 2 + -8x + -4x2 = (12 + 2x) Solving 2 + -8x + -4x2 = 12 + 2x Solving for variable 'x'. Reorder the terms: 2 + -12 + -8x + -2x + -4x2 = 12 + 2x + -12 + -2x Combine like terms: 2 + -12 = -10 -10 + -8x + -2x + -4x2 = 12 + 2x + -12 + -2x Combine like terms: -8x + -2x = -10x -10 + -10x + -4x2 = 12 + 2x + -12 + -2x Reorder the terms: -10 + -10x + -4x2 = 12 + -12 + 2x + -2x Combine like terms: 12 + -12 = 0 -10 + -10x + -4x2 = 0 + 2x + -2x -10 + -10x + -4x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -10 + -10x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(5 + 5x + 2x2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(5 + 5x + 2x2)' equal to zero and attempt to solve: Simplifying 5 + 5x + 2x2 = 0 Solving 5 + 5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 2.5x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 2.5x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 2.5x + x2 = 0 + -2.5 2.5x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 2.5x + x2 = -2.5 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = -2.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = -2.5 + 1.5625 Combine like terms: -2.5 + 1.5625 = -0.9375 1.5625 + 2.5x + x2 = -0.9375 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = -0.9375 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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