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Simplifying -9x(x + -4) + 8 = 4(3x + -2) + 8 Reorder the terms: -9x(-4 + x) + 8 = 4(3x + -2) + 8 (-4 * -9x + x * -9x) + 8 = 4(3x + -2) + 8 (36x + -9x2) + 8 = 4(3x + -2) + 8 Reorder the terms: 8 + 36x + -9x2 = 4(3x + -2) + 8 Reorder the terms: 8 + 36x + -9x2 = 4(-2 + 3x) + 8 8 + 36x + -9x2 = (-2 * 4 + 3x * 4) + 8 8 + 36x + -9x2 = (-8 + 12x) + 8 Reorder the terms: 8 + 36x + -9x2 = -8 + 8 + 12x Combine like terms: -8 + 8 = 0 8 + 36x + -9x2 = 0 + 12x 8 + 36x + -9x2 = 12x Solving 8 + 36x + -9x2 = 12x Solving for variable 'x'. Reorder the terms: 8 + 36x + -12x + -9x2 = 12x + -12x Combine like terms: 36x + -12x = 24x 8 + 24x + -9x2 = 12x + -12x Combine like terms: 12x + -12x = 0 8 + 24x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.8888888889 + -2.666666667x + x2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + -2.666666667x + 0.8888888889 + x2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + -2.666666667x + x2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + -2.666666667x + x2 = 0 + 0.8888888889 -2.666666667x + x2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 -2.666666667x + x2 = 0.8888888889 The x term is -2.666666667x. Take half its coefficient (-1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. -2.666666667x + 1.777777780 + x2 = 0.8888888889 + 1.777777780 Reorder the terms: 1.777777780 + -2.666666667x + x2 = 0.8888888889 + 1.777777780 Combine like terms: 0.8888888889 + 1.777777780 = 2.6666666689 1.777777780 + -2.666666667x + x2 = 2.6666666689 Factor a perfect square on the left side: (x + -1.333333334)(x + -1.333333334) = 2.6666666689 Calculate the square root of the right side: 1.632993163 Break this problem into two subproblems by setting (x + -1.333333334) equal to 1.632993163 and -1.632993163.Subproblem 1
x + -1.333333334 = 1.632993163 Simplifying x + -1.333333334 = 1.632993163 Reorder the terms: -1.333333334 + x = 1.632993163 Solving -1.333333334 + x = 1.632993163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = 1.632993163 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 1.632993163 + 1.333333334 x = 1.632993163 + 1.333333334 Combine like terms: 1.632993163 + 1.333333334 = 2.966326497 x = 2.966326497 Simplifying x = 2.966326497Subproblem 2
x + -1.333333334 = -1.632993163 Simplifying x + -1.333333334 = -1.632993163 Reorder the terms: -1.333333334 + x = -1.632993163 Solving -1.333333334 + x = -1.632993163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = -1.632993163 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -1.632993163 + 1.333333334 x = -1.632993163 + 1.333333334 Combine like terms: -1.632993163 + 1.333333334 = -0.299659829 x = -0.299659829 Simplifying x = -0.299659829Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.966326497, -0.299659829}
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