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Simplifying 0 = 9x2 + 5x + 2 Reorder the terms: 0 = 2 + 5x + 9x2 Solving 0 = 2 + 5x + 9x2 Solving for variable 'x'. Combine like terms: 0 + -2 = -2 -2 + -5x + -9x2 = 2 + 5x + 9x2 + -2 + -5x + -9x2 Reorder the terms: -2 + -5x + -9x2 = 2 + -2 + 5x + -5x + 9x2 + -9x2 Combine like terms: 2 + -2 = 0 -2 + -5x + -9x2 = 0 + 5x + -5x + 9x2 + -9x2 -2 + -5x + -9x2 = 5x + -5x + 9x2 + -9x2 Combine like terms: 5x + -5x = 0 -2 + -5x + -9x2 = 0 + 9x2 + -9x2 -2 + -5x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -2 + -5x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 5x + 9x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 5x + 9x2)' equal to zero and attempt to solve: Simplifying 2 + 5x + 9x2 = 0 Solving 2 + 5x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.2222222222 + 0.5555555556x + x2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + 0.5555555556x + -0.2222222222 + x2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + 0.5555555556x + x2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + 0.5555555556x + x2 = 0 + -0.2222222222 0.5555555556x + x2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 0.5555555556x + x2 = -0.2222222222 The x term is 0.5555555556x. Take half its coefficient (0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. 0.5555555556x + 0.07716049384 + x2 = -0.2222222222 + 0.07716049384 Reorder the terms: 0.07716049384 + 0.5555555556x + x2 = -0.2222222222 + 0.07716049384 Combine like terms: -0.2222222222 + 0.07716049384 = -0.14506172836 0.07716049384 + 0.5555555556x + x2 = -0.14506172836 Factor a perfect square on the left side: (x + 0.2777777778)(x + 0.2777777778) = -0.14506172836 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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