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Simplifying 256x2 + 10 = x2 + 5x Reorder the terms: 10 + 256x2 = x2 + 5x Reorder the terms: 10 + 256x2 = 5x + x2 Solving 10 + 256x2 = 5x + x2 Solving for variable 'x'. Reorder the terms: 10 + -5x + 256x2 + -1x2 = 5x + x2 + -5x + -1x2 Combine like terms: 256x2 + -1x2 = 255x2 10 + -5x + 255x2 = 5x + x2 + -5x + -1x2 Reorder the terms: 10 + -5x + 255x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 10 + -5x + 255x2 = 0 + x2 + -1x2 10 + -5x + 255x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 10 + -5x + 255x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(2 + -1x + 51x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2 + -1x + 51x2)' equal to zero and attempt to solve: Simplifying 2 + -1x + 51x2 = 0 Solving 2 + -1x + 51x2 = 0 Begin completing the square. Divide all terms by 51 the coefficient of the squared term: Divide each side by '51'. 0.03921568627 + -0.01960784314x + x2 = 0 Move the constant term to the right: Add '-0.03921568627' to each side of the equation. 0.03921568627 + -0.01960784314x + -0.03921568627 + x2 = 0 + -0.03921568627 Reorder the terms: 0.03921568627 + -0.03921568627 + -0.01960784314x + x2 = 0 + -0.03921568627 Combine like terms: 0.03921568627 + -0.03921568627 = 0.00000000000 0.00000000000 + -0.01960784314x + x2 = 0 + -0.03921568627 -0.01960784314x + x2 = 0 + -0.03921568627 Combine like terms: 0 + -0.03921568627 = -0.03921568627 -0.01960784314x + x2 = -0.03921568627 The x term is -0.01960784314x. Take half its coefficient (-0.00980392157). Square it (0.00009611687815) and add it to both sides. Add '0.00009611687815' to each side of the equation. -0.01960784314x + 0.00009611687815 + x2 = -0.03921568627 + 0.00009611687815 Reorder the terms: 0.00009611687815 + -0.01960784314x + x2 = -0.03921568627 + 0.00009611687815 Combine like terms: -0.03921568627 + 0.00009611687815 = -0.03911956939185 0.00009611687815 + -0.01960784314x + x2 = -0.03911956939185 Factor a perfect square on the left side: (x + -0.00980392157)(x + -0.00980392157) = -0.03911956939185 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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