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Simplifying 2x4 + -2x2 + -15 = 0 Reorder the terms: -15 + -2x2 + 2x4 = 0 Solving -15 + -2x2 + 2x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7.5 + -1x2 + x4 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -1x2 + 7.5 + x4 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -1x2 + x4 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -1x2 + x4 = 0 + 7.5 -1x2 + x4 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -1x2 + x4 = 7.5 The x term is -1x2. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x2 + 0.25 + x4 = 7.5 + 0.25 Reorder the terms: 0.25 + -1x2 + x4 = 7.5 + 0.25 Combine like terms: 7.5 + 0.25 = 7.75 0.25 + -1x2 + x4 = 7.75 Factor a perfect square on the left side: (x2 + -0.5)(x2 + -0.5) = 7.75 Calculate the square root of the right side: 2.783882181 Break this problem into two subproblems by setting (x2 + -0.5) equal to 2.783882181 and -2.783882181.Subproblem 1
x2 + -0.5 = 2.783882181 Simplifying x2 + -0.5 = 2.783882181 Reorder the terms: -0.5 + x2 = 2.783882181 Solving -0.5 + x2 = 2.783882181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x2 = 2.783882181 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = 2.783882181 + 0.5 x2 = 2.783882181 + 0.5 Combine like terms: 2.783882181 + 0.5 = 3.283882181 x2 = 3.283882181 Simplifying x2 = 3.283882181 Take the square root of each side: x = {-1.812148499, 1.812148499}Subproblem 2
x2 + -0.5 = -2.783882181 Simplifying x2 + -0.5 = -2.783882181 Reorder the terms: -0.5 + x2 = -2.783882181 Solving -0.5 + x2 = -2.783882181 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x2 = -2.783882181 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = -2.783882181 + 0.5 x2 = -2.783882181 + 0.5 Combine like terms: -2.783882181 + 0.5 = -2.283882181 x2 = -2.283882181 Simplifying x2 = -2.283882181 Reorder the terms: 2.283882181 + x2 = -2.283882181 + 2.283882181 Combine like terms: -2.283882181 + 2.283882181 = 0.000000000 2.283882181 + 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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