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Simplifying -2x2 = -1x4 + x3 + 2x2 Reorder the terms: -2x2 = 2x2 + x3 + -1x4 Solving -2x2 = 2x2 + x3 + -1x4 Solving for variable 'x'. Combine like terms: -2x2 + -2x2 = -4x2 -4x2 + -1x3 + x4 = 2x2 + x3 + -1x4 + -2x2 + -1x3 + x4 Reorder the terms: -4x2 + -1x3 + x4 = 2x2 + -2x2 + x3 + -1x3 + -1x4 + x4 Combine like terms: 2x2 + -2x2 = 0 -4x2 + -1x3 + x4 = 0 + x3 + -1x3 + -1x4 + x4 -4x2 + -1x3 + x4 = x3 + -1x3 + -1x4 + x4 Combine like terms: x3 + -1x3 = 0 -4x2 + -1x3 + x4 = 0 + -1x4 + x4 -4x2 + -1x3 + x4 = -1x4 + x4 Combine like terms: -1x4 + x4 = 0 -4x2 + -1x3 + x4 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(-4 + -1x + 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 + -1x + x2)' equal to zero and attempt to solve: Simplifying -4 + -1x + x2 = 0 Solving -4 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -1x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -1x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1x + x2 = 0 + 4 -1x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -1x + x2 = 4 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 4 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 4 + 0.25 Combine like terms: 4 + 0.25 = 4.25 0.25 + -1x + x2 = 4.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + -0.5) equal to 2.061552813 and -2.061552813.Subproblem 1
x + -0.5 = 2.061552813 Simplifying x + -0.5 = 2.061552813 Reorder the terms: -0.5 + x = 2.061552813 Solving -0.5 + x = 2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 2.061552813 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.061552813 + 0.5 x = 2.061552813 + 0.5 Combine like terms: 2.061552813 + 0.5 = 2.561552813 x = 2.561552813 Simplifying x = 2.561552813Subproblem 2
x + -0.5 = -2.061552813 Simplifying x + -0.5 = -2.061552813 Reorder the terms: -0.5 + x = -2.061552813 Solving -0.5 + x = -2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -2.061552813 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.061552813 + 0.5 x = -2.061552813 + 0.5 Combine like terms: -2.061552813 + 0.5 = -1.561552813 x = -1.561552813 Simplifying x = -1.561552813Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.561552813, -1.561552813}Solution
x = {0, 2.561552813, -1.561552813}
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