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Simplifying (8x3 + -4x2 + x) + -1(2x3 + 9x2 + 4x) = 0 Reorder the terms: (x + -4x2 + 8x3) + -1(2x3 + 9x2 + 4x) = 0 Remove parenthesis around (x + -4x2 + 8x3) x + -4x2 + 8x3 + -1(2x3 + 9x2 + 4x) = 0 Reorder the terms: x + -4x2 + 8x3 + -1(4x + 9x2 + 2x3) = 0 x + -4x2 + 8x3 + (4x * -1 + 9x2 * -1 + 2x3 * -1) = 0 x + -4x2 + 8x3 + (-4x + -9x2 + -2x3) = 0 Reorder the terms: x + -4x + -4x2 + -9x2 + 8x3 + -2x3 = 0 Combine like terms: x + -4x = -3x -3x + -4x2 + -9x2 + 8x3 + -2x3 = 0 Combine like terms: -4x2 + -9x2 = -13x2 -3x + -13x2 + 8x3 + -2x3 = 0 Combine like terms: 8x3 + -2x3 = 6x3 -3x + -13x2 + 6x3 = 0 Solving -3x + -13x2 + 6x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-3 + -13x + 6x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-3 + -13x + 6x2)' equal to zero and attempt to solve: Simplifying -3 + -13x + 6x2 = 0 Solving -3 + -13x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.5 + -2.166666667x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -2.166666667x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -2.166666667x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -2.166666667x + x2 = 0 + 0.5 -2.166666667x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -2.166666667x + x2 = 0.5 The x term is -2.166666667x. Take half its coefficient (-1.083333334). Square it (1.173611113) and add it to both sides. Add '1.173611113' to each side of the equation. -2.166666667x + 1.173611113 + x2 = 0.5 + 1.173611113 Reorder the terms: 1.173611113 + -2.166666667x + x2 = 0.5 + 1.173611113 Combine like terms: 0.5 + 1.173611113 = 1.673611113 1.173611113 + -2.166666667x + x2 = 1.673611113 Factor a perfect square on the left side: (x + -1.083333334)(x + -1.083333334) = 1.673611113 Calculate the square root of the right side: 1.293681225 Break this problem into two subproblems by setting (x + -1.083333334) equal to 1.293681225 and -1.293681225.Subproblem 1
x + -1.083333334 = 1.293681225 Simplifying x + -1.083333334 = 1.293681225 Reorder the terms: -1.083333334 + x = 1.293681225 Solving -1.083333334 + x = 1.293681225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + x = 1.293681225 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = 1.293681225 + 1.083333334 x = 1.293681225 + 1.083333334 Combine like terms: 1.293681225 + 1.083333334 = 2.377014559 x = 2.377014559 Simplifying x = 2.377014559Subproblem 2
x + -1.083333334 = -1.293681225 Simplifying x + -1.083333334 = -1.293681225 Reorder the terms: -1.083333334 + x = -1.293681225 Solving -1.083333334 + x = -1.293681225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + x = -1.293681225 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = -1.293681225 + 1.083333334 x = -1.293681225 + 1.083333334 Combine like terms: -1.293681225 + 1.083333334 = -0.210347891 x = -0.210347891 Simplifying x = -0.210347891Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.377014559, -0.210347891}Solution
x = {0, 2.377014559, -0.210347891}
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