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Simplifying 36x2 + -54x + -3636x2 + -54x + -36 = 0 Reorder the terms: -36 + -54x + -54x + 36x2 + -3636x2 = 0 Combine like terms: -54x + -54x = -108x -36 + -108x + 36x2 + -3636x2 = 0 Combine like terms: 36x2 + -3636x2 = -3600x2 -36 + -108x + -3600x2 = 0 Solving -36 + -108x + -3600x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-36'. -36(1 + 3x + 100x2) = 0 Ignore the factor -36.Subproblem 1
Set the factor '(1 + 3x + 100x2)' equal to zero and attempt to solve: Simplifying 1 + 3x + 100x2 = 0 Solving 1 + 3x + 100x2 = 0 Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. 0.01 + 0.03x + x2 = 0.00 Move the constant term to the right: Add '-0.01' to each side of the equation. 0.01 + 0.03x + -0.01 + x2 = 0.00 + -0.01 Reorder the terms: 0.01 + -0.01 + 0.03x + x2 = 0.00 + -0.01 Combine like terms: 0.01 + -0.01 = 0.00 0.00 + 0.03x + x2 = 0.00 + -0.01 0.03x + x2 = 0.00 + -0.01 Combine like terms: 0.00 + -0.01 = -0.01 0.03x + x2 = -0.01 The x term is 0.03x. Take half its coefficient (0.015). Square it (0.000225) and add it to both sides. Add '0.000225' to each side of the equation. 0.03x + 0.000225 + x2 = -0.01 + 0.000225 Reorder the terms: 0.000225 + 0.03x + x2 = -0.01 + 0.000225 Combine like terms: -0.01 + 0.000225 = -0.009775 0.000225 + 0.03x + x2 = -0.009775 Factor a perfect square on the left side: (x + 0.015)(x + 0.015) = -0.009775 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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