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Simplifying x8 + 15x4 + -6 = 0 Reorder the terms: -6 + 15x4 + x8 = 0 Solving -6 + 15x4 + x8 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 15x4 + 6 + x8 = 0 + 6 Reorder the terms: -6 + 6 + 15x4 + x8 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 15x4 + x8 = 0 + 6 15x4 + x8 = 0 + 6 Combine like terms: 0 + 6 = 6 15x4 + x8 = 6 The x term is 15x4. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x4 + 56.25 + x8 = 6 + 56.25 Reorder the terms: 56.25 + 15x4 + x8 = 6 + 56.25 Combine like terms: 6 + 56.25 = 62.25 56.25 + 15x4 + x8 = 62.25 Factor a perfect square on the left side: (x4 + 7.5)(x4 + 7.5) = 62.25 Calculate the square root of the right side: 7.889866919 Break this problem into two subproblems by setting (x4 + 7.5) equal to 7.889866919 and -7.889866919.Subproblem 1
x4 + 7.5 = 7.889866919 Simplifying x4 + 7.5 = 7.889866919 Reorder the terms: 7.5 + x4 = 7.889866919 Solving 7.5 + x4 = 7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x4 = 7.889866919 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x4 = 7.889866919 + -7.5 x4 = 7.889866919 + -7.5 Combine like terms: 7.889866919 + -7.5 = 0.389866919 x4 = 0.389866919 Simplifying x4 = 0.389866919 Reorder the terms: -0.389866919 + x4 = 0.389866919 + -0.389866919 Combine like terms: 0.389866919 + -0.389866919 = 0.000000000 -0.389866919 + x4 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x4 + 7.5 = -7.889866919 Simplifying x4 + 7.5 = -7.889866919 Reorder the terms: 7.5 + x4 = -7.889866919 Solving 7.5 + x4 = -7.889866919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x4 = -7.889866919 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x4 = -7.889866919 + -7.5 x4 = -7.889866919 + -7.5 Combine like terms: -7.889866919 + -7.5 = -15.389866919 x4 = -15.389866919 Simplifying x4 = -15.389866919 Reorder the terms: 15.389866919 + x4 = -15.389866919 + 15.389866919 Combine like terms: -15.389866919 + 15.389866919 = 0.000000000 15.389866919 + x4 = 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.
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