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