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Simplifying 7x2 + -32x + -6 = 0 Reorder the terms: -6 + -32x + 7x2 = 0 Solving -6 + -32x + 7x2 = 0 Solving for variable 'x'. 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 = 4.751810929 x = 4.751810929 Simplifying x = 4.751810929Subproblem 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 = -0.180382357 x = -0.180382357 Simplifying x = -0.180382357Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.751810929, -0.180382357}
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