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Simplifying -2(3x2 + 4) + -3(x2 + 2x) = 0 Reorder the terms: -2(4 + 3x2) + -3(x2 + 2x) = 0 (4 * -2 + 3x2 * -2) + -3(x2 + 2x) = 0 (-8 + -6x2) + -3(x2 + 2x) = 0 Reorder the terms: -8 + -6x2 + -3(2x + x2) = 0 -8 + -6x2 + (2x * -3 + x2 * -3) = 0 -8 + -6x2 + (-6x + -3x2) = 0 Reorder the terms: -8 + -6x + -6x2 + -3x2 = 0 Combine like terms: -6x2 + -3x2 = -9x2 -8 + -6x + -9x2 = 0 Solving -8 + -6x + -9x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 6x + 9x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(8 + 6x + 9x2)' equal to zero and attempt to solve: Simplifying 8 + 6x + 9x2 = 0 Solving 8 + 6x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.8888888889 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '-0.8888888889' to each side of the equation. 0.8888888889 + 0.6666666667x + -0.8888888889 + x2 = 0 + -0.8888888889 Reorder the terms: 0.8888888889 + -0.8888888889 + 0.6666666667x + x2 = 0 + -0.8888888889 Combine like terms: 0.8888888889 + -0.8888888889 = 0.0000000000 0.0000000000 + 0.6666666667x + x2 = 0 + -0.8888888889 0.6666666667x + x2 = 0 + -0.8888888889 Combine like terms: 0 + -0.8888888889 = -0.8888888889 0.6666666667x + x2 = -0.8888888889 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 = -0.8888888889 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = -0.8888888889 + 0.1111111112 Combine like terms: -0.8888888889 + 0.1111111112 = -0.7777777777 0.1111111112 + 0.6666666667x + x2 = -0.7777777777 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = -0.7777777777 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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