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Simplifying -2x(8x + -5) + 2x = 4(x + 5) Reorder the terms: -2x(-5 + 8x) + 2x = 4(x + 5) (-5 * -2x + 8x * -2x) + 2x = 4(x + 5) (10x + -16x2) + 2x = 4(x + 5) Reorder the terms: 10x + 2x + -16x2 = 4(x + 5) Combine like terms: 10x + 2x = 12x 12x + -16x2 = 4(x + 5) Reorder the terms: 12x + -16x2 = 4(5 + x) 12x + -16x2 = (5 * 4 + x * 4) 12x + -16x2 = (20 + 4x) Solving 12x + -16x2 = 20 + 4x Solving for variable 'x'. Reorder the terms: -20 + 12x + -4x + -16x2 = 20 + 4x + -20 + -4x Combine like terms: 12x + -4x = 8x -20 + 8x + -16x2 = 20 + 4x + -20 + -4x Reorder the terms: -20 + 8x + -16x2 = 20 + -20 + 4x + -4x Combine like terms: 20 + -20 = 0 -20 + 8x + -16x2 = 0 + 4x + -4x -20 + 8x + -16x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -20 + 8x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + 2x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + 2x + -4x2)' equal to zero and attempt to solve: Simplifying -5 + 2x + -4x2 = 0 Solving -5 + 2x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 1.25 + -0.5x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -0.5x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -0.5x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -0.5x + x2 = 0 + -1.25 -0.5x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -0.5x + x2 = -1.25 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = -1.25 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = -1.25 + 0.0625 Combine like terms: -1.25 + 0.0625 = -1.1875 0.0625 + -0.5x + x2 = -1.1875 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = -1.1875 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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