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Simplifying 10 = -4x(2x + -1) Reorder the terms: 10 = -4x(-1 + 2x) 10 = (-1 * -4x + 2x * -4x) 10 = (4x + -8x2) Solving 10 = 4x + -8x2 Solving for variable 'x'. Reorder the terms: 10 + -4x + 8x2 = 4x + -4x + -8x2 + 8x2 Combine like terms: 4x + -4x = 0 10 + -4x + 8x2 = 0 + -8x2 + 8x2 10 + -4x + 8x2 = -8x2 + 8x2 Combine like terms: -8x2 + 8x2 = 0 10 + -4x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -2x + 4x2) = 0 Ignore the factor 2.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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