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Simplifying x4 + -17x2 + 64 = 0 Reorder the terms: 64 + -17x2 + x4 = 0 Solving 64 + -17x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-64' to each side of the equation. 64 + -17x2 + -64 + x4 = 0 + -64 Reorder the terms: 64 + -64 + -17x2 + x4 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + -17x2 + x4 = 0 + -64 -17x2 + x4 = 0 + -64 Combine like terms: 0 + -64 = -64 -17x2 + x4 = -64 The x term is -17x2. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x2 + 72.25 + x4 = -64 + 72.25 Reorder the terms: 72.25 + -17x2 + x4 = -64 + 72.25 Combine like terms: -64 + 72.25 = 8.25 72.25 + -17x2 + x4 = 8.25 Factor a perfect square on the left side: (x2 + -8.5)(x2 + -8.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (x2 + -8.5) equal to 2.872281323 and -2.872281323.Subproblem 1
x2 + -8.5 = 2.872281323 Simplifying x2 + -8.5 = 2.872281323 Reorder the terms: -8.5 + x2 = 2.872281323 Solving -8.5 + x2 = 2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x2 = 2.872281323 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x2 = 2.872281323 + 8.5 x2 = 2.872281323 + 8.5 Combine like terms: 2.872281323 + 8.5 = 11.372281323 x2 = 11.372281323 Simplifying x2 = 11.372281323 Take the square root of each side: x = {-3.372281323, 3.372281323}Subproblem 2
x2 + -8.5 = -2.872281323 Simplifying x2 + -8.5 = -2.872281323 Reorder the terms: -8.5 + x2 = -2.872281323 Solving -8.5 + x2 = -2.872281323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x2 = -2.872281323 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x2 = -2.872281323 + 8.5 x2 = -2.872281323 + 8.5 Combine like terms: -2.872281323 + 8.5 = 5.627718677 x2 = 5.627718677 Simplifying x2 = 5.627718677 Take the square root of each side: x = {-2.372281323, 2.372281323}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.372281323, 3.372281323, -2.372281323, 2.372281323}
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