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Simplifying 2x4 + -15x2 + -18 = 0 Reorder the terms: -18 + -15x2 + 2x4 = 0 Solving -18 + -15x2 + 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'. -9 + -7.5x2 + x4 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -7.5x2 + 9 + x4 = 0 + 9 Reorder the terms: -9 + 9 + -7.5x2 + x4 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -7.5x2 + x4 = 0 + 9 -7.5x2 + x4 = 0 + 9 Combine like terms: 0 + 9 = 9 -7.5x2 + x4 = 9 The x term is -7.5x2. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x2 + 14.0625 + x4 = 9 + 14.0625 Reorder the terms: 14.0625 + -7.5x2 + x4 = 9 + 14.0625 Combine like terms: 9 + 14.0625 = 23.0625 14.0625 + -7.5x2 + x4 = 23.0625 Factor a perfect square on the left side: (x2 + -3.75)(x2 + -3.75) = 23.0625 Calculate the square root of the right side: 4.802343178 Break this problem into two subproblems by setting (x2 + -3.75) equal to 4.802343178 and -4.802343178.Subproblem 1
x2 + -3.75 = 4.802343178 Simplifying x2 + -3.75 = 4.802343178 Reorder the terms: -3.75 + x2 = 4.802343178 Solving -3.75 + x2 = 4.802343178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x2 = 4.802343178 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x2 = 4.802343178 + 3.75 x2 = 4.802343178 + 3.75 Combine like terms: 4.802343178 + 3.75 = 8.552343178 x2 = 8.552343178 Simplifying x2 = 8.552343178 Take the square root of each side: x = {-2.924438951, 2.924438951}Subproblem 2
x2 + -3.75 = -4.802343178 Simplifying x2 + -3.75 = -4.802343178 Reorder the terms: -3.75 + x2 = -4.802343178 Solving -3.75 + x2 = -4.802343178 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x2 = -4.802343178 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x2 = -4.802343178 + 3.75 x2 = -4.802343178 + 3.75 Combine like terms: -4.802343178 + 3.75 = -1.052343178 x2 = -1.052343178 Simplifying x2 = -1.052343178 Reorder the terms: 1.052343178 + x2 = -1.052343178 + 1.052343178 Combine like terms: -1.052343178 + 1.052343178 = 0.000000000 1.052343178 + 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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