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Simplifying x4 + -3x2 + -8x3 = 0 Reorder the terms: -3x2 + -8x3 + x4 = 0 Solving -3x2 + -8x3 + x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(-3 + -8x + 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 '(-3 + -8x + x2)' equal to zero and attempt to solve: Simplifying -3 + -8x + x2 = 0 Solving -3 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -8x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -8x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -8x + x2 = 0 + 3 -8x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -8x + x2 = 3 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 3 + 16 Reorder the terms: 16 + -8x + x2 = 3 + 16 Combine like terms: 3 + 16 = 19 16 + -8x + x2 = 19 Factor a perfect square on the left side: (x + -4)(x + -4) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + -4) equal to 4.358898944 and -4.358898944.Subproblem 1
x + -4 = 4.358898944 Simplifying x + -4 = 4.358898944 Reorder the terms: -4 + x = 4.358898944 Solving -4 + x = 4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.358898944 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.358898944 + 4 x = 4.358898944 + 4 Combine like terms: 4.358898944 + 4 = 8.358898944 x = 8.358898944 Simplifying x = 8.358898944Subproblem 2
x + -4 = -4.358898944 Simplifying x + -4 = -4.358898944 Reorder the terms: -4 + x = -4.358898944 Solving -4 + x = -4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.358898944 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.358898944 + 4 x = -4.358898944 + 4 Combine like terms: -4.358898944 + 4 = -0.358898944 x = -0.358898944 Simplifying x = -0.358898944Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.358898944, -0.358898944}Solution
x = {0, 8.358898944, -0.358898944}
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