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Simplifying 2(9x2 + -5x + 6) = 0 Reorder the terms: 2(6 + -5x + 9x2) = 0 (6 * 2 + -5x * 2 + 9x2 * 2) = 0 (12 + -10x + 18x2) = 0 Solving 12 + -10x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(6 + -5x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + -5x + 9x2)' equal to zero and attempt to solve: Simplifying 6 + -5x + 9x2 = 0 Solving 6 + -5x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.6666666667 + -0.5555555556x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -0.5555555556x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -0.5555555556x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -0.5555555556x + x2 = 0 + -0.6666666667 -0.5555555556x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -0.5555555556x + x2 = -0.6666666667 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 = -0.6666666667 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556x + x2 = -0.6666666667 + 0.07716049384 Combine like terms: -0.6666666667 + 0.07716049384 = -0.58950617286 0.07716049384 + -0.5555555556x + x2 = -0.58950617286 Factor a perfect square on the left side: (x + -0.2777777778)(x + -0.2777777778) = -0.58950617286 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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