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Simplifying x(7x2 + -1x + -28 + -4) = 0 Reorder the terms: x(-28 + -4 + -1x + 7x2) = 0 Combine like terms: -28 + -4 = -32 x(-32 + -1x + 7x2) = 0 (-32 * x + -1x * x + 7x2 * x) = 0 (-32x + -1x2 + 7x3) = 0 Solving -32x + -1x2 + 7x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-32 + -1x + 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 '(-32 + -1x + 7x2)' equal to zero and attempt to solve: Simplifying -32 + -1x + 7x2 = 0 Solving -32 + -1x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -4.571428571 + -0.1428571429x + x2 = 0 Move the constant term to the right: Add '4.571428571' to each side of the equation. -4.571428571 + -0.1428571429x + 4.571428571 + x2 = 0 + 4.571428571 Reorder the terms: -4.571428571 + 4.571428571 + -0.1428571429x + x2 = 0 + 4.571428571 Combine like terms: -4.571428571 + 4.571428571 = 0.000000000 0.000000000 + -0.1428571429x + x2 = 0 + 4.571428571 -0.1428571429x + x2 = 0 + 4.571428571 Combine like terms: 0 + 4.571428571 = 4.571428571 -0.1428571429x + x2 = 4.571428571 The x term is -0.1428571429x. Take half its coefficient (-0.07142857145). Square it (0.005102040819) and add it to both sides. Add '0.005102040819' to each side of the equation. -0.1428571429x + 0.005102040819 + x2 = 4.571428571 + 0.005102040819 Reorder the terms: 0.005102040819 + -0.1428571429x + x2 = 4.571428571 + 0.005102040819 Combine like terms: 4.571428571 + 0.005102040819 = 4.576530611819 0.005102040819 + -0.1428571429x + x2 = 4.576530611819 Factor a perfect square on the left side: (x + -0.07142857145)(x + -0.07142857145) = 4.576530611819 Calculate the square root of the right side: 2.139282733 Break this problem into two subproblems by setting (x + -0.07142857145) equal to 2.139282733 and -2.139282733.Subproblem 1
x + -0.07142857145 = 2.139282733 Simplifying x + -0.07142857145 = 2.139282733 Reorder the terms: -0.07142857145 + x = 2.139282733 Solving -0.07142857145 + x = 2.139282733 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = 2.139282733 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = 2.139282733 + 0.07142857145 x = 2.139282733 + 0.07142857145 Combine like terms: 2.139282733 + 0.07142857145 = 2.21071130445 x = 2.21071130445 Simplifying x = 2.21071130445Subproblem 2
x + -0.07142857145 = -2.139282733 Simplifying x + -0.07142857145 = -2.139282733 Reorder the terms: -0.07142857145 + x = -2.139282733 Solving -0.07142857145 + x = -2.139282733 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = -2.139282733 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = -2.139282733 + 0.07142857145 x = -2.139282733 + 0.07142857145 Combine like terms: -2.139282733 + 0.07142857145 = -2.06785416155 x = -2.06785416155 Simplifying x = -2.06785416155Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.21071130445, -2.06785416155}Solution
x = {0, 2.21071130445, -2.06785416155}
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