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Simplifying 360x2 + -36x + 8 = 0 Reorder the terms: 8 + -36x + 360x2 = 0 Solving 8 + -36x + 360x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(2 + -9x + 90x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + -9x + 90x2)' equal to zero and attempt to solve: Simplifying 2 + -9x + 90x2 = 0 Solving 2 + -9x + 90x2 = 0 Begin completing the square. Divide all terms by 90 the coefficient of the squared term: Divide each side by '90'. 0.02222222222 + -0.1x + x2 = 0.0 Move the constant term to the right: Add '-0.02222222222' to each side of the equation. 0.02222222222 + -0.1x + -0.02222222222 + x2 = 0.0 + -0.02222222222 Reorder the terms: 0.02222222222 + -0.02222222222 + -0.1x + x2 = 0.0 + -0.02222222222 Combine like terms: 0.02222222222 + -0.02222222222 = 0.00000000000 0.00000000000 + -0.1x + x2 = 0.0 + -0.02222222222 -0.1x + x2 = 0.0 + -0.02222222222 Combine like terms: 0.0 + -0.02222222222 = -0.02222222222 -0.1x + x2 = -0.02222222222 The x term is -0.1x. Take half its coefficient (-0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. -0.1x + 0.0025 + x2 = -0.02222222222 + 0.0025 Reorder the terms: 0.0025 + -0.1x + x2 = -0.02222222222 + 0.0025 Combine like terms: -0.02222222222 + 0.0025 = -0.01972222222 0.0025 + -0.1x + x2 = -0.01972222222 Factor a perfect square on the left side: (x + -0.05)(x + -0.05) = -0.01972222222 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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