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Simplifying x4 + -7x2 + 7 = 0 Reorder the terms: 7 + -7x2 + x4 = 0 Solving 7 + -7x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -7x2 + -7 + x4 = 0 + -7 Reorder the terms: 7 + -7 + -7x2 + x4 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -7x2 + x4 = 0 + -7 -7x2 + x4 = 0 + -7 Combine like terms: 0 + -7 = -7 -7x2 + x4 = -7 The x term is -7x2. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x2 + 12.25 + x4 = -7 + 12.25 Reorder the terms: 12.25 + -7x2 + x4 = -7 + 12.25 Combine like terms: -7 + 12.25 = 5.25 12.25 + -7x2 + x4 = 5.25 Factor a perfect square on the left side: (x2 + -3.5)(x2 + -3.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x2 + -3.5) equal to 2.291287847 and -2.291287847.Subproblem 1
x2 + -3.5 = 2.291287847 Simplifying x2 + -3.5 = 2.291287847 Reorder the terms: -3.5 + x2 = 2.291287847 Solving -3.5 + x2 = 2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x2 = 2.291287847 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x2 = 2.291287847 + 3.5 x2 = 2.291287847 + 3.5 Combine like terms: 2.291287847 + 3.5 = 5.791287847 x2 = 5.791287847 Simplifying x2 = 5.791287847 Take the square root of each side: x = {-2.406509474, 2.406509474}Subproblem 2
x2 + -3.5 = -2.291287847 Simplifying x2 + -3.5 = -2.291287847 Reorder the terms: -3.5 + x2 = -2.291287847 Solving -3.5 + x2 = -2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x2 = -2.291287847 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x2 = -2.291287847 + 3.5 x2 = -2.291287847 + 3.5 Combine like terms: -2.291287847 + 3.5 = 1.208712153 x2 = 1.208712153 Simplifying x2 = 1.208712153 Take the square root of each side: x = {-1.099414459, 1.099414459}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.406509474, 2.406509474, -1.099414459, 1.099414459}
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