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Simplifying x4 + -4x3 = 4x2 Reorder the terms: -4x3 + x4 = 4x2 Solving -4x3 + x4 = 4x2 Solving for variable 'x'. Reorder the terms: -4x2 + -4x3 + x4 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -4x2 + -4x3 + x4 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(-4 + -4x + 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 '(-4 + -4x + x2)' equal to zero and attempt to solve: Simplifying -4 + -4x + x2 = 0 Solving -4 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -4x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -4x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -4x + x2 = 0 + 4 -4x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -4x + x2 = 4 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 4 + 4 Reorder the terms: 4 + -4x + x2 = 4 + 4 Combine like terms: 4 + 4 = 8 4 + -4x + x2 = 8 Factor a perfect square on the left side: (x + -2)(x + -2) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + -2) equal to 2.828427125 and -2.828427125.Subproblem 1
x + -2 = 2.828427125 Simplifying x + -2 = 2.828427125 Reorder the terms: -2 + x = 2.828427125 Solving -2 + x = 2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.828427125 + 2 x = 2.828427125 + 2 Combine like terms: 2.828427125 + 2 = 4.828427125 x = 4.828427125 Simplifying x = 4.828427125Subproblem 2
x + -2 = -2.828427125 Simplifying x + -2 = -2.828427125 Reorder the terms: -2 + x = -2.828427125 Solving -2 + x = -2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.828427125 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.828427125 + 2 x = -2.828427125 + 2 Combine like terms: -2.828427125 + 2 = -0.828427125 x = -0.828427125 Simplifying x = -0.828427125Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.828427125, -0.828427125}Solution
x = {0, 4.828427125, -0.828427125}
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