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Simplifying x4 + 6x2 + -1.75 = 0 Reorder the terms: -1.75 + 6x2 + x4 = 0 Solving -1.75 + 6x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + 6x2 + 1.75 + x4 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + 6x2 + x4 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + 6x2 + x4 = 0 + 1.75 6x2 + x4 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 6x2 + x4 = 1.75 The x term is 6x2. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x2 + 9 + x4 = 1.75 + 9 Reorder the terms: 9 + 6x2 + x4 = 1.75 + 9 Combine like terms: 1.75 + 9 = 10.75 9 + 6x2 + x4 = 10.75 Factor a perfect square on the left side: (x2 + 3)(x2 + 3) = 10.75 Calculate the square root of the right side: 3.278719262 Break this problem into two subproblems by setting (x2 + 3) equal to 3.278719262 and -3.278719262.Subproblem 1
x2 + 3 = 3.278719262 Simplifying x2 + 3 = 3.278719262 Reorder the terms: 3 + x2 = 3.278719262 Solving 3 + x2 = 3.278719262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x2 = 3.278719262 + -3 Combine like terms: 3 + -3 = 0 0 + x2 = 3.278719262 + -3 x2 = 3.278719262 + -3 Combine like terms: 3.278719262 + -3 = 0.278719262 x2 = 0.278719262 Simplifying x2 = 0.278719262 Take the square root of each side: x = {-0.527938692, 0.527938692}Subproblem 2
x2 + 3 = -3.278719262 Simplifying x2 + 3 = -3.278719262 Reorder the terms: 3 + x2 = -3.278719262 Solving 3 + x2 = -3.278719262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x2 = -3.278719262 + -3 Combine like terms: 3 + -3 = 0 0 + x2 = -3.278719262 + -3 x2 = -3.278719262 + -3 Combine like terms: -3.278719262 + -3 = -6.278719262 x2 = -6.278719262 Simplifying x2 = -6.278719262 Reorder the terms: 6.278719262 + x2 = -6.278719262 + 6.278719262 Combine like terms: -6.278719262 + 6.278719262 = 0.000000000 6.278719262 + 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.
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