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Simplifying 3(x4 + x2 + -24) = 0 Reorder the terms: 3(-24 + x2 + x4) = 0 (-24 * 3 + x2 * 3 + x4 * 3) = 0 (-72 + 3x2 + 3x4) = 0 Solving -72 + 3x2 + 3x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-24 + x2 + x4) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-24 + x2 + x4)' equal to zero and attempt to solve: Simplifying -24 + x2 + x4 = 0 Solving -24 + x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + x2 + 24 + x4 = 0 + 24 Reorder the terms: -24 + 24 + x2 + x4 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + x2 + x4 = 0 + 24 x2 + x4 = 0 + 24 Combine like terms: 0 + 24 = 24 x2 + x4 = 24 The x term is x2. 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. x2 + 0.25 + x4 = 24 + 0.25 Reorder the terms: 0.25 + x2 + x4 = 24 + 0.25 Combine like terms: 24 + 0.25 = 24.25 0.25 + x2 + x4 = 24.25 Factor a perfect square on the left side: (x2 + 0.5)(x2 + 0.5) = 24.25 Calculate the square root of the right side: 4.924428901 Break this problem into two subproblems by setting (x2 + 0.5) equal to 4.924428901 and -4.924428901.Subproblem 1
x2 + 0.5 = 4.924428901 Simplifying x2 + 0.5 = 4.924428901 Reorder the terms: 0.5 + x2 = 4.924428901 Solving 0.5 + x2 = 4.924428901 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 + x2 = 4.924428901 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = 4.924428901 + -0.5 x2 = 4.924428901 + -0.5 Combine like terms: 4.924428901 + -0.5 = 4.424428901 x2 = 4.424428901 Simplifying x2 = 4.424428901 Take the square root of each side: x = {-2.103432647, 2.103432647}Subproblem 2
x2 + 0.5 = -4.924428901 Simplifying x2 + 0.5 = -4.924428901 Reorder the terms: 0.5 + x2 = -4.924428901 Solving 0.5 + x2 = -4.924428901 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 + x2 = -4.924428901 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x2 = -4.924428901 + -0.5 x2 = -4.924428901 + -0.5 Combine like terms: -4.924428901 + -0.5 = -5.424428901 x2 = -5.424428901 Simplifying x2 = -5.424428901 Reorder the terms: 5.424428901 + x2 = -5.424428901 + 5.424428901 Combine like terms: -5.424428901 + 5.424428901 = 0.000000000 5.424428901 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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