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Simplifying 6(9x2 + 6x + 1) + -5 + 7 = 0 Reorder the terms: 6(1 + 6x + 9x2) + -5 + 7 = 0 (1 * 6 + 6x * 6 + 9x2 * 6) + -5 + 7 = 0 (6 + 36x + 54x2) + -5 + 7 = 0 Reorder the terms: 6 + -5 + 7 + 36x + 54x2 = 0 Combine like terms: 6 + -5 = 1 1 + 7 + 36x + 54x2 = 0 Combine like terms: 1 + 7 = 8 8 + 36x + 54x2 = 0 Solving 8 + 36x + 54x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 18x + 27x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + 18x + 27x2)' equal to zero and attempt to solve: Simplifying 4 + 18x + 27x2 = 0 Solving 4 + 18x + 27x2 = 0 Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. 0.1481481481 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '-0.1481481481' to each side of the equation. 0.1481481481 + 0.6666666667x + -0.1481481481 + x2 = 0 + -0.1481481481 Reorder the terms: 0.1481481481 + -0.1481481481 + 0.6666666667x + x2 = 0 + -0.1481481481 Combine like terms: 0.1481481481 + -0.1481481481 = 0.0000000000 0.0000000000 + 0.6666666667x + x2 = 0 + -0.1481481481 0.6666666667x + x2 = 0 + -0.1481481481 Combine like terms: 0 + -0.1481481481 = -0.1481481481 0.6666666667x + x2 = -0.1481481481 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = -0.1481481481 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = -0.1481481481 + 0.1111111112 Combine like terms: -0.1481481481 + 0.1111111112 = -0.0370370369 0.1111111112 + 0.6666666667x + x2 = -0.0370370369 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = -0.0370370369 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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