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Simplifying 100x2 + 50x + 625 = 0 Reorder the terms: 625 + 50x + 100x2 = 0 Solving 625 + 50x + 100x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '25'. 25(25 + 2x + 4x2) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(25 + 2x + 4x2)' equal to zero and attempt to solve: Simplifying 25 + 2x + 4x2 = 0 Solving 25 + 2x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6.25 + 0.5x + x2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + 0.5x + -6.25 + x2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + 0.5x + x2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + 0.5x + x2 = 0 + -6.25 0.5x + x2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 0.5x + x2 = -6.25 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 = -6.25 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = -6.25 + 0.0625 Combine like terms: -6.25 + 0.0625 = -6.1875 0.0625 + 0.5x + x2 = -6.1875 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = -6.1875 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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