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Simplifying x4 + -23x2 + 40 = 0 Reorder the terms: 40 + -23x2 + x4 = 0 Solving 40 + -23x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + -23x2 + -40 + x4 = 0 + -40 Reorder the terms: 40 + -40 + -23x2 + x4 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -23x2 + x4 = 0 + -40 -23x2 + x4 = 0 + -40 Combine like terms: 0 + -40 = -40 -23x2 + x4 = -40 The x term is -23x2. Take half its coefficient (-11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. -23x2 + 132.25 + x4 = -40 + 132.25 Reorder the terms: 132.25 + -23x2 + x4 = -40 + 132.25 Combine like terms: -40 + 132.25 = 92.25 132.25 + -23x2 + x4 = 92.25 Factor a perfect square on the left side: (x2 + -11.5)(x2 + -11.5) = 92.25 Calculate the square root of the right side: 9.604686356 Break this problem into two subproblems by setting (x2 + -11.5) equal to 9.604686356 and -9.604686356.Subproblem 1
x2 + -11.5 = 9.604686356 Simplifying x2 + -11.5 = 9.604686356 Reorder the terms: -11.5 + x2 = 9.604686356 Solving -11.5 + x2 = 9.604686356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x2 = 9.604686356 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x2 = 9.604686356 + 11.5 x2 = 9.604686356 + 11.5 Combine like terms: 9.604686356 + 11.5 = 21.104686356 x2 = 21.104686356 Simplifying x2 = 21.104686356 Take the square root of each side: x = {-4.593983713, 4.593983713}Subproblem 2
x2 + -11.5 = -9.604686356 Simplifying x2 + -11.5 = -9.604686356 Reorder the terms: -11.5 + x2 = -9.604686356 Solving -11.5 + x2 = -9.604686356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x2 = -9.604686356 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x2 = -9.604686356 + 11.5 x2 = -9.604686356 + 11.5 Combine like terms: -9.604686356 + 11.5 = 1.895313644 x2 = 1.895313644 Simplifying x2 = 1.895313644 Take the square root of each side: x = {-1.376703906, 1.376703906}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.593983713, 4.593983713, -1.376703906, 1.376703906}
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