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Simplifying 7x3 + 32x2 + -6x = 0 Reorder the terms: -6x + 32x2 + 7x3 = 0 Solving -6x + 32x2 + 7x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-6 + 32x + 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 + 32x + 7x2)' equal to zero and attempt to solve: Simplifying -6 + 32x + 7x2 = 0 Solving -6 + 32x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.8571428571 + 4.571428571x + x2 = 0 Move the constant term to the right: Add '0.8571428571' to each side of the equation. -0.8571428571 + 4.571428571x + 0.8571428571 + x2 = 0 + 0.8571428571 Reorder the terms: -0.8571428571 + 0.8571428571 + 4.571428571x + x2 = 0 + 0.8571428571 Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000 0.0000000000 + 4.571428571x + x2 = 0 + 0.8571428571 4.571428571x + x2 = 0 + 0.8571428571 Combine like terms: 0 + 0.8571428571 = 0.8571428571 4.571428571x + x2 = 0.8571428571 The x term is 4.571428571x. Take half its coefficient (2.285714286). Square it (5.224489797) and add it to both sides. Add '5.224489797' to each side of the equation. 4.571428571x + 5.224489797 + x2 = 0.8571428571 + 5.224489797 Reorder the terms: 5.224489797 + 4.571428571x + x2 = 0.8571428571 + 5.224489797 Combine like terms: 0.8571428571 + 5.224489797 = 6.0816326541 5.224489797 + 4.571428571x + x2 = 6.0816326541 Factor a perfect square on the left side: (x + 2.285714286)(x + 2.285714286) = 6.0816326541 Calculate the square root of the right side: 2.466096643 Break this problem into two subproblems by setting (x + 2.285714286) equal to 2.466096643 and -2.466096643.Subproblem 1
x + 2.285714286 = 2.466096643 Simplifying x + 2.285714286 = 2.466096643 Reorder the terms: 2.285714286 + x = 2.466096643 Solving 2.285714286 + x = 2.466096643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.285714286' to each side of the equation. 2.285714286 + -2.285714286 + x = 2.466096643 + -2.285714286 Combine like terms: 2.285714286 + -2.285714286 = 0.000000000 0.000000000 + x = 2.466096643 + -2.285714286 x = 2.466096643 + -2.285714286 Combine like terms: 2.466096643 + -2.285714286 = 0.180382357 x = 0.180382357 Simplifying x = 0.180382357Subproblem 2
x + 2.285714286 = -2.466096643 Simplifying x + 2.285714286 = -2.466096643 Reorder the terms: 2.285714286 + x = -2.466096643 Solving 2.285714286 + x = -2.466096643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.285714286' to each side of the equation. 2.285714286 + -2.285714286 + x = -2.466096643 + -2.285714286 Combine like terms: 2.285714286 + -2.285714286 = 0.000000000 0.000000000 + x = -2.466096643 + -2.285714286 x = -2.466096643 + -2.285714286 Combine like terms: -2.466096643 + -2.285714286 = -4.751810929 x = -4.751810929 Simplifying x = -4.751810929Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.180382357, -4.751810929}Solution
x = {0, 0.180382357, -4.751810929}
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