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Simplifying x4 + 10x3 = -2x2 Reorder the terms: 10x3 + x4 = -2x2 Solving 10x3 + x4 = -2x2 Solving for variable 'x'. Reorder the terms: 2x2 + 10x3 + x4 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 2x2 + 10x3 + x4 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(2 + 10x + x2) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(2 + 10x + x2)' equal to zero and attempt to solve: Simplifying 2 + 10x + x2 = 0 Solving 2 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 10x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 10x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 10x + x2 = 0 + -2 10x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 10x + x2 = -2 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -2 + 25 Reorder the terms: 25 + 10x + x2 = -2 + 25 Combine like terms: -2 + 25 = 23 25 + 10x + x2 = 23 Factor a perfect square on the left side: (x + 5)(x + 5) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (x + 5) equal to 4.795831523 and -4.795831523.Subproblem 1
x + 5 = 4.795831523 Simplifying x + 5 = 4.795831523 Reorder the terms: 5 + x = 4.795831523 Solving 5 + x = 4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 4.795831523 + -5 Combine like terms: 5 + -5 = 0 0 + x = 4.795831523 + -5 x = 4.795831523 + -5 Combine like terms: 4.795831523 + -5 = -0.204168477 x = -0.204168477 Simplifying x = -0.204168477Subproblem 2
x + 5 = -4.795831523 Simplifying x + 5 = -4.795831523 Reorder the terms: 5 + x = -4.795831523 Solving 5 + x = -4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -4.795831523 + -5 Combine like terms: 5 + -5 = 0 0 + x = -4.795831523 + -5 x = -4.795831523 + -5 Combine like terms: -4.795831523 + -5 = -9.795831523 x = -9.795831523 Simplifying x = -9.795831523Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.204168477, -9.795831523}Solution
x = {0, -0.204168477, -9.795831523}
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