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Simplifying 5x4 + -18x2 + 1 = 0 Reorder the terms: 1 + -18x2 + 5x4 = 0 Solving 1 + -18x2 + 5x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + -3.6x2 + x4 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -3.6x2 + -0.2 + x4 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -3.6x2 + x4 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -3.6x2 + x4 = 0 + -0.2 -3.6x2 + x4 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -3.6x2 + x4 = -0.2 The x term is -3.6x2. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6x2 + 3.24 + x4 = -0.2 + 3.24 Reorder the terms: 3.24 + -3.6x2 + x4 = -0.2 + 3.24 Combine like terms: -0.2 + 3.24 = 3.04 3.24 + -3.6x2 + x4 = 3.04 Factor a perfect square on the left side: (x2 + -1.8)(x2 + -1.8) = 3.04 Calculate the square root of the right side: 1.743559577 Break this problem into two subproblems by setting (x2 + -1.8) equal to 1.743559577 and -1.743559577.Subproblem 1
x2 + -1.8 = 1.743559577 Simplifying x2 + -1.8 = 1.743559577 Reorder the terms: -1.8 + x2 = 1.743559577 Solving -1.8 + x2 = 1.743559577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x2 = 1.743559577 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x2 = 1.743559577 + 1.8 x2 = 1.743559577 + 1.8 Combine like terms: 1.743559577 + 1.8 = 3.543559577 x2 = 3.543559577 Simplifying x2 = 3.543559577 Take the square root of each side: x = {-1.882434481, 1.882434481}Subproblem 2
x2 + -1.8 = -1.743559577 Simplifying x2 + -1.8 = -1.743559577 Reorder the terms: -1.8 + x2 = -1.743559577 Solving -1.8 + x2 = -1.743559577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x2 = -1.743559577 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x2 = -1.743559577 + 1.8 x2 = -1.743559577 + 1.8 Combine like terms: -1.743559577 + 1.8 = 0.056440423 x2 = 0.056440423 Simplifying x2 = 0.056440423 Take the square root of each side: x = {-0.237571932, 0.237571932}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.882434481, 1.882434481, -0.237571932, 0.237571932}
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