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Simplifying 0 = 4x2 + 8x + 125 Reorder the terms: 0 = 125 + 8x + 4x2 Solving 0 = 125 + 8x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -125 = -125 -125 + -8x + -4x2 = 125 + 8x + 4x2 + -125 + -8x + -4x2 Reorder the terms: -125 + -8x + -4x2 = 125 + -125 + 8x + -8x + 4x2 + -4x2 Combine like terms: 125 + -125 = 0 -125 + -8x + -4x2 = 0 + 8x + -8x + 4x2 + -4x2 -125 + -8x + -4x2 = 8x + -8x + 4x2 + -4x2 Combine like terms: 8x + -8x = 0 -125 + -8x + -4x2 = 0 + 4x2 + -4x2 -125 + -8x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -125 + -8x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(125 + 8x + 4x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(125 + 8x + 4x2)' equal to zero and attempt to solve: Simplifying 125 + 8x + 4x2 = 0 Solving 125 + 8x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 31.25 + 2x + x2 = 0 Move the constant term to the right: Add '-31.25' to each side of the equation. 31.25 + 2x + -31.25 + x2 = 0 + -31.25 Reorder the terms: 31.25 + -31.25 + 2x + x2 = 0 + -31.25 Combine like terms: 31.25 + -31.25 = 0.00 0.00 + 2x + x2 = 0 + -31.25 2x + x2 = 0 + -31.25 Combine like terms: 0 + -31.25 = -31.25 2x + x2 = -31.25 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -31.25 + 1 Reorder the terms: 1 + 2x + x2 = -31.25 + 1 Combine like terms: -31.25 + 1 = -30.25 1 + 2x + x2 = -30.25 Factor a perfect square on the left side: (x + 1)(x + 1) = -30.25 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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