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Simplifying (2x3 + -5x2 + 5x) + (5x3 + 9x2 + -11x) = 0 Reorder the terms: (5x + -5x2 + 2x3) + (5x3 + 9x2 + -11x) = 0 Remove parenthesis around (5x + -5x2 + 2x3) 5x + -5x2 + 2x3 + (5x3 + 9x2 + -11x) = 0 Reorder the terms: 5x + -5x2 + 2x3 + (-11x + 9x2 + 5x3) = 0 Remove parenthesis around (-11x + 9x2 + 5x3) 5x + -5x2 + 2x3 + -11x + 9x2 + 5x3 = 0 Reorder the terms: 5x + -11x + -5x2 + 9x2 + 2x3 + 5x3 = 0 Combine like terms: 5x + -11x = -6x -6x + -5x2 + 9x2 + 2x3 + 5x3 = 0 Combine like terms: -5x2 + 9x2 = 4x2 -6x + 4x2 + 2x3 + 5x3 = 0 Combine like terms: 2x3 + 5x3 = 7x3 -6x + 4x2 + 7x3 = 0 Solving -6x + 4x2 + 7x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-6 + 4x + 7x2) = 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 '(-6 + 4x + 7x2)' equal to zero and attempt to solve: Simplifying -6 + 4x + 7x2 = 0 Solving -6 + 4x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.8571428571 + 0.5714285714x + x2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + 0.5714285714x + 0.8571428571 + x2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + 0.5714285714x + x2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + 0.5714285714x + x2 = 0 + 0.8571428571 0.5714285714x + x2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 0.5714285714x + x2 = 0.8571428571 The x term is 0.5714285714x. Take half its coefficient (0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. 0.5714285714x + 0.08163265305 + x2 = 0.8571428571 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714x + x2 = 0.8571428571 + 0.08163265305 Combine like terms: 0.8571428571 + 0.08163265305 = 0.93877551015 0.08163265305 + 0.5714285714x + x2 = 0.93877551015 Factor a perfect square on the left side: (x + 0.2857142857)(x + 0.2857142857) = 0.93877551015 Calculate the square root of the right side: 0.968904283 Break this problem into two subproblems by setting (x + 0.2857142857) equal to 0.968904283 and -0.968904283.Subproblem 1
x + 0.2857142857 = 0.968904283 Simplifying x + 0.2857142857 = 0.968904283 Reorder the terms: 0.2857142857 + x = 0.968904283 Solving 0.2857142857 + x = 0.968904283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = 0.968904283 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = 0.968904283 + -0.2857142857 x = 0.968904283 + -0.2857142857 Combine like terms: 0.968904283 + -0.2857142857 = 0.6831899973 x = 0.6831899973 Simplifying x = 0.6831899973Subproblem 2
x + 0.2857142857 = -0.968904283 Simplifying x + 0.2857142857 = -0.968904283 Reorder the terms: 0.2857142857 + x = -0.968904283 Solving 0.2857142857 + x = -0.968904283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2857142857' to each side of the equation. 0.2857142857 + -0.2857142857 + x = -0.968904283 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + x = -0.968904283 + -0.2857142857 x = -0.968904283 + -0.2857142857 Combine like terms: -0.968904283 + -0.2857142857 = -1.2546185687 x = -1.2546185687 Simplifying x = -1.2546185687Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6831899973, -1.2546185687}Solution
x = {0, 0.6831899973, -1.2546185687}
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