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Simplifying x3 + 2x2 + -10x = 0 Reorder the terms: -10x + 2x2 + x3 = 0 Solving -10x + 2x2 + x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-10 + 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 '(-10 + 2x + x2)' equal to zero and attempt to solve: Simplifying -10 + 2x + x2 = 0 Solving -10 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 2x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 2x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 2x + x2 = 0 + 10 2x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 2x + x2 = 10 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 = 10 + 1 Reorder the terms: 1 + 2x + x2 = 10 + 1 Combine like terms: 10 + 1 = 11 1 + 2x + x2 = 11 Factor a perfect square on the left side: (x + 1)(x + 1) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + 1) equal to 3.31662479 and -3.31662479.Subproblem 1
x + 1 = 3.31662479 Simplifying x + 1 = 3.31662479 Reorder the terms: 1 + x = 3.31662479 Solving 1 + x = 3.31662479 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 = 3.31662479 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.31662479 + -1 x = 3.31662479 + -1 Combine like terms: 3.31662479 + -1 = 2.31662479 x = 2.31662479 Simplifying x = 2.31662479Subproblem 2
x + 1 = -3.31662479 Simplifying x + 1 = -3.31662479 Reorder the terms: 1 + x = -3.31662479 Solving 1 + x = -3.31662479 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 = -3.31662479 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.31662479 + -1 x = -3.31662479 + -1 Combine like terms: -3.31662479 + -1 = -4.31662479 x = -4.31662479 Simplifying x = -4.31662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.31662479, -4.31662479}Solution
x = {0, 2.31662479, -4.31662479}
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