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Simplifying (4 + -9x)(3x + 2) = 500 Reorder the terms: (4 + -9x)(2 + 3x) = 500 Multiply (4 + -9x) * (2 + 3x) (4(2 + 3x) + -9x * (2 + 3x)) = 500 ((2 * 4 + 3x * 4) + -9x * (2 + 3x)) = 500 ((8 + 12x) + -9x * (2 + 3x)) = 500 (8 + 12x + (2 * -9x + 3x * -9x)) = 500 (8 + 12x + (-18x + -27x2)) = 500 Combine like terms: 12x + -18x = -6x (8 + -6x + -27x2) = 500 Solving 8 + -6x + -27x2 = 500 Solving for variable 'x'. Reorder the terms: 8 + -500 + -6x + -27x2 = 500 + -500 Combine like terms: 8 + -500 = -492 -492 + -6x + -27x2 = 500 + -500 Combine like terms: 500 + -500 = 0 -492 + -6x + -27x2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(164 + 2x + 9x2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(164 + 2x + 9x2)' equal to zero and attempt to solve: Simplifying 164 + 2x + 9x2 = 0 Solving 164 + 2x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 18.22222222 + 0.2222222222x + x2 = 0 Move the constant term to the right: Add '-18.22222222' to each side of the equation. 18.22222222 + 0.2222222222x + -18.22222222 + x2 = 0 + -18.22222222 Reorder the terms: 18.22222222 + -18.22222222 + 0.2222222222x + x2 = 0 + -18.22222222 Combine like terms: 18.22222222 + -18.22222222 = 0.00000000 0.00000000 + 0.2222222222x + x2 = 0 + -18.22222222 0.2222222222x + x2 = 0 + -18.22222222 Combine like terms: 0 + -18.22222222 = -18.22222222 0.2222222222x + x2 = -18.22222222 The x term is 0.2222222222x. Take half its coefficient (0.1111111111). Square it (0.01234567901) and add it to both sides. Add '0.01234567901' to each side of the equation. 0.2222222222x + 0.01234567901 + x2 = -18.22222222 + 0.01234567901 Reorder the terms: 0.01234567901 + 0.2222222222x + x2 = -18.22222222 + 0.01234567901 Combine like terms: -18.22222222 + 0.01234567901 = -18.20987654099 0.01234567901 + 0.2222222222x + x2 = -18.20987654099 Factor a perfect square on the left side: (x + 0.1111111111)(x + 0.1111111111) = -18.20987654099 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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