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Simplifying x4 + 30x2 = 125 Reorder the terms: 30x2 + x4 = 125 Solving 30x2 + x4 = 125 Solving for variable 'x'. Reorder the terms: -125 + 30x2 + x4 = 125 + -125 Combine like terms: 125 + -125 = 0 -125 + 30x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '125' to each side of the equation. -125 + 30x2 + 125 + x4 = 0 + 125 Reorder the terms: -125 + 125 + 30x2 + x4 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + 30x2 + x4 = 0 + 125 30x2 + x4 = 0 + 125 Combine like terms: 0 + 125 = 125 30x2 + x4 = 125 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 = 125 + 225 Reorder the terms: 225 + 30x2 + x4 = 125 + 225 Combine like terms: 125 + 225 = 350 225 + 30x2 + x4 = 350 Factor a perfect square on the left side: (x2 + 15)(x2 + 15) = 350 Calculate the square root of the right side: 18.708286934 Break this problem into two subproblems by setting (x2 + 15) equal to 18.708286934 and -18.708286934.Subproblem 1
x2 + 15 = 18.708286934 Simplifying x2 + 15 = 18.708286934 Reorder the terms: 15 + x2 = 18.708286934 Solving 15 + x2 = 18.708286934 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 = 18.708286934 + -15 Combine like terms: 15 + -15 = 0 0 + x2 = 18.708286934 + -15 x2 = 18.708286934 + -15 Combine like terms: 18.708286934 + -15 = 3.708286934 x2 = 3.708286934 Simplifying x2 = 3.708286934 Take the square root of each side: x = {-1.925691287, 1.925691287}Subproblem 2
x2 + 15 = -18.708286934 Simplifying x2 + 15 = -18.708286934 Reorder the terms: 15 + x2 = -18.708286934 Solving 15 + x2 = -18.708286934 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 = -18.708286934 + -15 Combine like terms: 15 + -15 = 0 0 + x2 = -18.708286934 + -15 x2 = -18.708286934 + -15 Combine like terms: -18.708286934 + -15 = -33.708286934 x2 = -33.708286934 Simplifying x2 = -33.708286934 Reorder the terms: 33.708286934 + x2 = -33.708286934 + 33.708286934 Combine like terms: -33.708286934 + 33.708286934 = 0.000000000 33.708286934 + 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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