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Simplifying 18x2 + 18x + 20 = 0 Reorder the terms: 20 + 18x + 18x2 = 0 Solving 20 + 18x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(10 + 9x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(10 + 9x + 9x2)' equal to zero and attempt to solve: Simplifying 10 + 9x + 9x2 = 0 Solving 10 + 9x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 1.111111111 + x + x2 = 0 Move the constant term to the right: Add '-1.111111111' to each side of the equation. 1.111111111 + x + -1.111111111 + x2 = 0 + -1.111111111 Reorder the terms: 1.111111111 + -1.111111111 + x + x2 = 0 + -1.111111111 Combine like terms: 1.111111111 + -1.111111111 = 0.000000000 0.000000000 + x + x2 = 0 + -1.111111111 x + x2 = 0 + -1.111111111 Combine like terms: 0 + -1.111111111 = -1.111111111 x + x2 = -1.111111111 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = -1.111111111 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -1.111111111 + 0.25 Combine like terms: -1.111111111 + 0.25 = -0.861111111 1.25 + x2 = -0.861111111 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.861111111 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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