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Simplifying x4 + -23x2 + 49 = 0 Reorder the terms: 49 + -23x2 + x4 = 0 Solving 49 + -23x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-49' to each side of the equation. 49 + -23x2 + -49 + x4 = 0 + -49 Reorder the terms: 49 + -49 + -23x2 + x4 = 0 + -49 Combine like terms: 49 + -49 = 0 0 + -23x2 + x4 = 0 + -49 -23x2 + x4 = 0 + -49 Combine like terms: 0 + -49 = -49 -23x2 + x4 = -49 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 = -49 + 132.25 Reorder the terms: 132.25 + -23x2 + x4 = -49 + 132.25 Combine like terms: -49 + 132.25 = 83.25 132.25 + -23x2 + x4 = 83.25 Factor a perfect square on the left side: (x2 + -11.5)(x2 + -11.5) = 83.25 Calculate the square root of the right side: 9.124143795 Break this problem into two subproblems by setting (x2 + -11.5) equal to 9.124143795 and -9.124143795.Subproblem 1
x2 + -11.5 = 9.124143795 Simplifying x2 + -11.5 = 9.124143795 Reorder the terms: -11.5 + x2 = 9.124143795 Solving -11.5 + x2 = 9.124143795 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 = 9.124143795 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x2 = 9.124143795 + 11.5 x2 = 9.124143795 + 11.5 Combine like terms: 9.124143795 + 11.5 = 20.624143795 x2 = 20.624143795 Simplifying x2 = 20.624143795 Take the square root of each side: x = {-4.541381265, 4.541381265}Subproblem 2
x2 + -11.5 = -9.124143795 Simplifying x2 + -11.5 = -9.124143795 Reorder the terms: -11.5 + x2 = -9.124143795 Solving -11.5 + x2 = -9.124143795 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 = -9.124143795 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x2 = -9.124143795 + 11.5 x2 = -9.124143795 + 11.5 Combine like terms: -9.124143795 + 11.5 = 2.375856205 x2 = 2.375856205 Simplifying x2 = 2.375856205 Take the square root of each side: x = {-1.541381265, 1.541381265}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.541381265, 4.541381265, -1.541381265, 1.541381265}
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