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Simplifying x4 + -9x2 + 15 = 0 Reorder the terms: 15 + -9x2 + x4 = 0 Solving 15 + -9x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + -9x2 + -15 + x4 = 0 + -15 Reorder the terms: 15 + -15 + -9x2 + x4 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -9x2 + x4 = 0 + -15 -9x2 + x4 = 0 + -15 Combine like terms: 0 + -15 = -15 -9x2 + x4 = -15 The x term is -9x2. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x2 + 20.25 + x4 = -15 + 20.25 Reorder the terms: 20.25 + -9x2 + x4 = -15 + 20.25 Combine like terms: -15 + 20.25 = 5.25 20.25 + -9x2 + x4 = 5.25 Factor a perfect square on the left side: (x2 + -4.5)(x2 + -4.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x2 + -4.5) equal to 2.291287847 and -2.291287847.Subproblem 1
x2 + -4.5 = 2.291287847 Simplifying x2 + -4.5 = 2.291287847 Reorder the terms: -4.5 + x2 = 2.291287847 Solving -4.5 + x2 = 2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x2 = 2.291287847 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x2 = 2.291287847 + 4.5 x2 = 2.291287847 + 4.5 Combine like terms: 2.291287847 + 4.5 = 6.791287847 x2 = 6.791287847 Simplifying x2 = 6.791287847 Take the square root of each side: x = {-2.606009948, 2.606009948}Subproblem 2
x2 + -4.5 = -2.291287847 Simplifying x2 + -4.5 = -2.291287847 Reorder the terms: -4.5 + x2 = -2.291287847 Solving -4.5 + x2 = -2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x2 = -2.291287847 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x2 = -2.291287847 + 4.5 x2 = -2.291287847 + 4.5 Combine like terms: -2.291287847 + 4.5 = 2.208712153 x2 = 2.208712153 Simplifying x2 = 2.208712153 Take the square root of each side: x = {-1.486173662, 1.486173662}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.606009948, 2.606009948, -1.486173662, 1.486173662}
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