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Simplifying x3 + 2x2 + -52x = 0 Reorder the terms: -52x + 2x2 + x3 = 0 Solving -52x + 2x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-52 + 2x + x2) = 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 '(-52 + 2x + x2)' equal to zero and attempt to solve: Simplifying -52 + 2x + x2 = 0 Solving -52 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + 2x + 52 + x2 = 0 + 52 Reorder the terms: -52 + 52 + 2x + x2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + 2x + x2 = 0 + 52 2x + x2 = 0 + 52 Combine like terms: 0 + 52 = 52 2x + x2 = 52 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 52 + 1 Reorder the terms: 1 + 2x + x2 = 52 + 1 Combine like terms: 52 + 1 = 53 1 + 2x + x2 = 53 Factor a perfect square on the left side: (x + 1)(x + 1) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (x + 1) equal to 7.280109889 and -7.280109889.Subproblem 1
x + 1 = 7.280109889 Simplifying x + 1 = 7.280109889 Reorder the terms: 1 + x = 7.280109889 Solving 1 + x = 7.280109889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 7.280109889 + -1 Combine like terms: 1 + -1 = 0 0 + x = 7.280109889 + -1 x = 7.280109889 + -1 Combine like terms: 7.280109889 + -1 = 6.280109889 x = 6.280109889 Simplifying x = 6.280109889Subproblem 2
x + 1 = -7.280109889 Simplifying x + 1 = -7.280109889 Reorder the terms: 1 + x = -7.280109889 Solving 1 + x = -7.280109889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -7.280109889 + -1 Combine like terms: 1 + -1 = 0 0 + x = -7.280109889 + -1 x = -7.280109889 + -1 Combine like terms: -7.280109889 + -1 = -8.280109889 x = -8.280109889 Simplifying x = -8.280109889Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.280109889, -8.280109889}Solution
x = {0, 6.280109889, -8.280109889}
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