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Simplifying x4 + -1x2 + 0.245 = 0 Reorder the terms: 0.245 + -1x2 + x4 = 0 Solving 0.245 + -1x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.245' to each side of the equation. 0.245 + -1x2 + -0.245 + x4 = 0 + -0.245 Reorder the terms: 0.245 + -0.245 + -1x2 + x4 = 0 + -0.245 Combine like terms: 0.245 + -0.245 = 0.000 0.000 + -1x2 + x4 = 0 + -0.245 -1x2 + x4 = 0 + -0.245 Combine like terms: 0 + -0.245 = -0.245 -1x2 + x4 = -0.245 The x term is -1x2. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x2 + 0.25 + x4 = -0.245 + 0.25 Reorder the terms: 0.25 + -1x2 + x4 = -0.245 + 0.25 Combine like terms: -0.245 + 0.25 = 0.005 0.25 + -1x2 + x4 = 0.005 Factor a perfect square on the left side: (x2 + -0.5)(x2 + -0.5) = 0.005 Calculate the square root of the right side: 0.070710678 Break this problem into two subproblems by setting (x2 + -0.5) equal to 0.070710678 and -0.070710678.Subproblem 1
x2 + -0.5 = 0.070710678 Simplifying x2 + -0.5 = 0.070710678 Reorder the terms: -0.5 + x2 = 0.070710678 Solving -0.5 + x2 = 0.070710678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x2 = 0.070710678 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = 0.070710678 + 0.5 x2 = 0.070710678 + 0.5 Combine like terms: 0.070710678 + 0.5 = 0.570710678 x2 = 0.570710678 Simplifying x2 = 0.570710678 Take the square root of each side: x = {-0.755453955, 0.755453955}Subproblem 2
x2 + -0.5 = -0.070710678 Simplifying x2 + -0.5 = -0.070710678 Reorder the terms: -0.5 + x2 = -0.070710678 Solving -0.5 + x2 = -0.070710678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x2 = -0.070710678 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = -0.070710678 + 0.5 x2 = -0.070710678 + 0.5 Combine like terms: -0.070710678 + 0.5 = 0.429289322 x2 = 0.429289322 Simplifying x2 = 0.429289322 Take the square root of each side: x = {-0.655201741, 0.655201741}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.755453955, 0.755453955, -0.655201741, 0.655201741}
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