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Simplifying 5x4 + 15x2 + -40 = 0 Reorder the terms: -40 + 15x2 + 5x4 = 0 Solving -40 + 15x2 + 5x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-8 + 3x2 + x4) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-8 + 3x2 + x4)' equal to zero and attempt to solve: Simplifying -8 + 3x2 + x4 = 0 Solving -8 + 3x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 3x2 + 8 + x4 = 0 + 8 Reorder the terms: -8 + 8 + 3x2 + x4 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 3x2 + x4 = 0 + 8 3x2 + x4 = 0 + 8 Combine like terms: 0 + 8 = 8 3x2 + x4 = 8 The x term is 3x2. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x2 + 2.25 + x4 = 8 + 2.25 Reorder the terms: 2.25 + 3x2 + x4 = 8 + 2.25 Combine like terms: 8 + 2.25 = 10.25 2.25 + 3x2 + x4 = 10.25 Factor a perfect square on the left side: (x2 + 1.5)(x2 + 1.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x2 + 1.5) equal to 3.201562119 and -3.201562119.Subproblem 1
x2 + 1.5 = 3.201562119 Simplifying x2 + 1.5 = 3.201562119 Reorder the terms: 1.5 + x2 = 3.201562119 Solving 1.5 + x2 = 3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x2 = 3.201562119 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x2 = 3.201562119 + -1.5 x2 = 3.201562119 + -1.5 Combine like terms: 3.201562119 + -1.5 = 1.701562119 x2 = 1.701562119 Simplifying x2 = 1.701562119 Take the square root of each side: x = {-1.304439389, 1.304439389}Subproblem 2
x2 + 1.5 = -3.201562119 Simplifying x2 + 1.5 = -3.201562119 Reorder the terms: 1.5 + x2 = -3.201562119 Solving 1.5 + x2 = -3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x2 = -3.201562119 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x2 = -3.201562119 + -1.5 x2 = -3.201562119 + -1.5 Combine like terms: -3.201562119 + -1.5 = -4.701562119 x2 = -4.701562119 Simplifying x2 = -4.701562119 Reorder the terms: 4.701562119 + x2 = -4.701562119 + 4.701562119 Combine like terms: -4.701562119 + 4.701562119 = 0.000000000 4.701562119 + 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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