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Simplifying (-1x + -2)(-1x + -2) + -1(4x + -1x)(4x + -1x) = 12 Reorder the terms: (-2 + -1x)(-1x + -2) + -1(4x + -1x)(4x + -1x) = 12 Reorder the terms: (-2 + -1x)(-2 + -1x) + -1(4x + -1x)(4x + -1x) = 12 Multiply (-2 + -1x) * (-2 + -1x) (-2(-2 + -1x) + -1x * (-2 + -1x)) + -1(4x + -1x)(4x + -1x) = 12 ((-2 * -2 + -1x * -2) + -1x * (-2 + -1x)) + -1(4x + -1x)(4x + -1x) = 12 ((4 + 2x) + -1x * (-2 + -1x)) + -1(4x + -1x)(4x + -1x) = 12 (4 + 2x + (-2 * -1x + -1x * -1x)) + -1(4x + -1x)(4x + -1x) = 12 (4 + 2x + (2x + 1x2)) + -1(4x + -1x)(4x + -1x) = 12 Combine like terms: 2x + 2x = 4x (4 + 4x + 1x2) + -1(4x + -1x)(4x + -1x) = 12 Combine like terms: 4x + -1x = 3x 4 + 4x + 1x2 + -1(3x)(4x + -1x) = 12 Remove parenthesis around (3x) 4 + 4x + 1x2 + -1 * 3x(4x + -1x) = 12 Combine like terms: 4x + -1x = 3x 4 + 4x + 1x2 + -1 * 3x(3x) = 12 Remove parenthesis around (3x) 4 + 4x + 1x2 + -1 * 3x * 3x = 12 Reorder the terms for easier multiplication: 4 + 4x + 1x2 + -1 * 3 * 3x * x = 12 Multiply -1 * 3 4 + 4x + 1x2 + -3 * 3x * x = 12 Multiply -3 * 3 4 + 4x + 1x2 + -9x * x = 12 Multiply x * x 4 + 4x + 1x2 + -9x2 = 12 Combine like terms: 1x2 + -9x2 = -8x2 4 + 4x + -8x2 = 12 Solving 4 + 4x + -8x2 = 12 Solving for variable 'x'. Reorder the terms: 4 + -12 + 4x + -8x2 = 12 + -12 Combine like terms: 4 + -12 = -8 -8 + 4x + -8x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -8 + 4x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-2 + x + -2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2 + x + -2x2)' equal to zero and attempt to solve: Simplifying -2 + x + -2x2 = 0 Solving -2 + x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 1 + -0.5x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -0.5x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -0.5x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -0.5x + x2 = 0 + -1 -0.5x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -0.5x + x2 = -1 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. -0.5x + 0.25 + x2 = -1 + 0.25 Reorder the terms: 0.25 + -0.5x + x2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + -0.5x + x2 = -0.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -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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