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Simplifying (4x + -1)(4x + -1) + 9 = 0 Reorder the terms: (-1 + 4x)(4x + -1) + 9 = 0 Reorder the terms: (-1 + 4x)(-1 + 4x) + 9 = 0 Multiply (-1 + 4x) * (-1 + 4x) (-1(-1 + 4x) + 4x * (-1 + 4x)) + 9 = 0 ((-1 * -1 + 4x * -1) + 4x * (-1 + 4x)) + 9 = 0 ((1 + -4x) + 4x * (-1 + 4x)) + 9 = 0 (1 + -4x + (-1 * 4x + 4x * 4x)) + 9 = 0 (1 + -4x + (-4x + 16x2)) + 9 = 0 Combine like terms: -4x + -4x = -8x (1 + -8x + 16x2) + 9 = 0 Reorder the terms: 1 + 9 + -8x + 16x2 = 0 Combine like terms: 1 + 9 = 10 10 + -8x + 16x2 = 0 Solving 10 + -8x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -4x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -4x + 8x2)' equal to zero and attempt to solve: Simplifying 5 + -4x + 8x2 = 0 Solving 5 + -4x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.625 + -0.5x + x2 = 0 Move the constant term to the right: Add '-0.625' to each side of the equation. 0.625 + -0.5x + -0.625 + x2 = 0 + -0.625 Reorder the terms: 0.625 + -0.625 + -0.5x + x2 = 0 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + -0.5x + x2 = 0 + -0.625 -0.5x + x2 = 0 + -0.625 Combine like terms: 0 + -0.625 = -0.625 -0.5x + x2 = -0.625 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 = -0.625 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = -0.625 + 0.0625 Combine like terms: -0.625 + 0.0625 = -0.5625 0.0625 + -0.5x + x2 = -0.5625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = -0.5625 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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