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Simplifying x4 + -59x2 + 289 = 0 Reorder the terms: 289 + -59x2 + x4 = 0 Solving 289 + -59x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-289' to each side of the equation. 289 + -59x2 + -289 + x4 = 0 + -289 Reorder the terms: 289 + -289 + -59x2 + x4 = 0 + -289 Combine like terms: 289 + -289 = 0 0 + -59x2 + x4 = 0 + -289 -59x2 + x4 = 0 + -289 Combine like terms: 0 + -289 = -289 -59x2 + x4 = -289 The x term is -59x2. Take half its coefficient (-29.5). Square it (870.25) and add it to both sides. Add '870.25' to each side of the equation. -59x2 + 870.25 + x4 = -289 + 870.25 Reorder the terms: 870.25 + -59x2 + x4 = -289 + 870.25 Combine like terms: -289 + 870.25 = 581.25 870.25 + -59x2 + x4 = 581.25 Factor a perfect square on the left side: (x2 + -29.5)(x2 + -29.5) = 581.25 Calculate the square root of the right side: 24.109126902 Break this problem into two subproblems by setting (x2 + -29.5) equal to 24.109126902 and -24.109126902.Subproblem 1
x2 + -29.5 = 24.109126902 Simplifying x2 + -29.5 = 24.109126902 Reorder the terms: -29.5 + x2 = 24.109126902 Solving -29.5 + x2 = 24.109126902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '29.5' to each side of the equation. -29.5 + 29.5 + x2 = 24.109126902 + 29.5 Combine like terms: -29.5 + 29.5 = 0.0 0.0 + x2 = 24.109126902 + 29.5 x2 = 24.109126902 + 29.5 Combine like terms: 24.109126902 + 29.5 = 53.609126902 x2 = 53.609126902 Simplifying x2 = 53.609126902 Take the square root of each side: x = {-7.32182538, 7.32182538}Subproblem 2
x2 + -29.5 = -24.109126902 Simplifying x2 + -29.5 = -24.109126902 Reorder the terms: -29.5 + x2 = -24.109126902 Solving -29.5 + x2 = -24.109126902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '29.5' to each side of the equation. -29.5 + 29.5 + x2 = -24.109126902 + 29.5 Combine like terms: -29.5 + 29.5 = 0.0 0.0 + x2 = -24.109126902 + 29.5 x2 = -24.109126902 + 29.5 Combine like terms: -24.109126902 + 29.5 = 5.390873098 x2 = 5.390873098 Simplifying x2 = 5.390873098 Take the square root of each side: x = {-2.321825381, 2.321825381}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-7.32182538, 7.32182538, -2.321825381, 2.321825381}
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