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Simplifying x4 + 30x2 + -10 = 0 Reorder the terms: -10 + 30x2 + x4 = 0 Solving -10 + 30x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 30x2 + 10 + x4 = 0 + 10 Reorder the terms: -10 + 10 + 30x2 + x4 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 30x2 + x4 = 0 + 10 30x2 + x4 = 0 + 10 Combine like terms: 0 + 10 = 10 30x2 + x4 = 10 The x term is 30x2. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x2 + 225 + x4 = 10 + 225 Reorder the terms: 225 + 30x2 + x4 = 10 + 225 Combine like terms: 10 + 225 = 235 225 + 30x2 + x4 = 235 Factor a perfect square on the left side: (x2 + 15)(x2 + 15) = 235 Calculate the square root of the right side: 15.329709717 Break this problem into two subproblems by setting (x2 + 15) equal to 15.329709717 and -15.329709717.Subproblem 1
x2 + 15 = 15.329709717 Simplifying x2 + 15 = 15.329709717 Reorder the terms: 15 + x2 = 15.329709717 Solving 15 + x2 = 15.329709717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x2 = 15.329709717 + -15 Combine like terms: 15 + -15 = 0 0 + x2 = 15.329709717 + -15 x2 = 15.329709717 + -15 Combine like terms: 15.329709717 + -15 = 0.329709717 x2 = 0.329709717 Simplifying x2 = 0.329709717 Take the square root of each side: x = {-0.57420355, 0.57420355}Subproblem 2
x2 + 15 = -15.329709717 Simplifying x2 + 15 = -15.329709717 Reorder the terms: 15 + x2 = -15.329709717 Solving 15 + x2 = -15.329709717 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x2 = -15.329709717 + -15 Combine like terms: 15 + -15 = 0 0 + x2 = -15.329709717 + -15 x2 = -15.329709717 + -15 Combine like terms: -15.329709717 + -15 = -30.329709717 x2 = -30.329709717 Simplifying x2 = -30.329709717 Reorder the terms: 30.329709717 + x2 = -30.329709717 + 30.329709717 Combine like terms: -30.329709717 + 30.329709717 = 0.000000000 30.329709717 + 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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