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Simplifying 15x4 + -75x2 + -60 = 0 Reorder the terms: -60 + -75x2 + 15x4 = 0 Solving -60 + -75x2 + 15x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '15'. 15(-4 + -5x2 + x4) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(-4 + -5x2 + x4)' equal to zero and attempt to solve: Simplifying -4 + -5x2 + x4 = 0 Solving -4 + -5x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -5x2 + 4 + x4 = 0 + 4 Reorder the terms: -4 + 4 + -5x2 + x4 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5x2 + x4 = 0 + 4 -5x2 + x4 = 0 + 4 Combine like terms: 0 + 4 = 4 -5x2 + x4 = 4 The x term is -5x2. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x2 + 6.25 + x4 = 4 + 6.25 Reorder the terms: 6.25 + -5x2 + x4 = 4 + 6.25 Combine like terms: 4 + 6.25 = 10.25 6.25 + -5x2 + x4 = 10.25 Factor a perfect square on the left side: (x2 + -2.5)(x2 + -2.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x2 + -2.5) equal to 3.201562119 and -3.201562119.Subproblem 1
x2 + -2.5 = 3.201562119 Simplifying x2 + -2.5 = 3.201562119 Reorder the terms: -2.5 + x2 = 3.201562119 Solving -2.5 + x2 = 3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x2 = 3.201562119 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x2 = 3.201562119 + 2.5 x2 = 3.201562119 + 2.5 Combine like terms: 3.201562119 + 2.5 = 5.701562119 x2 = 5.701562119 Simplifying x2 = 5.701562119 Take the square root of each side: x = {-2.387794405, 2.387794405}Subproblem 2
x2 + -2.5 = -3.201562119 Simplifying x2 + -2.5 = -3.201562119 Reorder the terms: -2.5 + x2 = -3.201562119 Solving -2.5 + x2 = -3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x2 = -3.201562119 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x2 = -3.201562119 + 2.5 x2 = -3.201562119 + 2.5 Combine like terms: -3.201562119 + 2.5 = -0.701562119 x2 = -0.701562119 Simplifying x2 = -0.701562119 Reorder the terms: 0.701562119 + x2 = -0.701562119 + 0.701562119 Combine like terms: -0.701562119 + 0.701562119 = 0.000000000 0.701562119 + 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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