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Simplifying x4 + -1.36x2 + 1 = 0.909 Reorder the terms: 1 + -1.36x2 + x4 = 0.909 Solving 1 + -1.36x2 + x4 = 0.909 Solving for variable 'x'. Reorder the terms: 1 + -0.909 + -1.36x2 + x4 = 0.909 + -0.909 Combine like terms: 1 + -0.909 = 0.091 0.091 + -1.36x2 + x4 = 0.909 + -0.909 Combine like terms: 0.909 + -0.909 = 0.000 0.091 + -1.36x2 + x4 = 0.000 Begin completing the square. Move the constant term to the right: Add '-0.091' to each side of the equation. 0.091 + -1.36x2 + -0.091 + x4 = 0.000 + -0.091 Reorder the terms: 0.091 + -0.091 + -1.36x2 + x4 = 0.000 + -0.091 Combine like terms: 0.091 + -0.091 = 0.000 0.000 + -1.36x2 + x4 = 0.000 + -0.091 -1.36x2 + x4 = 0.000 + -0.091 Combine like terms: 0.000 + -0.091 = -0.091 -1.36x2 + x4 = -0.091 The x term is -1.36x2. Take half its coefficient (-0.68). Square it (0.4624) and add it to both sides. Add '0.4624' to each side of the equation. -1.36x2 + 0.4624 + x4 = -0.091 + 0.4624 Reorder the terms: 0.4624 + -1.36x2 + x4 = -0.091 + 0.4624 Combine like terms: -0.091 + 0.4624 = 0.3714 0.4624 + -1.36x2 + x4 = 0.3714 Factor a perfect square on the left side: (x2 + -0.68)(x2 + -0.68) = 0.3714 Calculate the square root of the right side: 0.609425959 Break this problem into two subproblems by setting (x2 + -0.68) equal to 0.609425959 and -0.609425959.Subproblem 1
x2 + -0.68 = 0.609425959 Simplifying x2 + -0.68 = 0.609425959 Reorder the terms: -0.68 + x2 = 0.609425959 Solving -0.68 + x2 = 0.609425959 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.68' to each side of the equation. -0.68 + 0.68 + x2 = 0.609425959 + 0.68 Combine like terms: -0.68 + 0.68 = 0.00 0.00 + x2 = 0.609425959 + 0.68 x2 = 0.609425959 + 0.68 Combine like terms: 0.609425959 + 0.68 = 1.289425959 x2 = 1.289425959 Simplifying x2 = 1.289425959 Take the square root of each side: x = {-1.135528934, 1.135528934}Subproblem 2
x2 + -0.68 = -0.609425959 Simplifying x2 + -0.68 = -0.609425959 Reorder the terms: -0.68 + x2 = -0.609425959 Solving -0.68 + x2 = -0.609425959 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.68' to each side of the equation. -0.68 + 0.68 + x2 = -0.609425959 + 0.68 Combine like terms: -0.68 + 0.68 = 0.00 0.00 + x2 = -0.609425959 + 0.68 x2 = -0.609425959 + 0.68 Combine like terms: -0.609425959 + 0.68 = 0.070574041 x2 = 0.070574041 Simplifying x2 = 0.070574041 Take the square root of each side: x = {-0.265657752, 0.265657752}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.135528934, 1.135528934, -0.265657752, 0.265657752}
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