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Simplifying x4 + -1(50x2) + 6 = 0 Remove parenthesis around (50x2) x4 + -1 * 50x2 + 6 = 0 Multiply -1 * 50 x4 + -50x2 + 6 = 0 Reorder the terms: 6 + -50x2 + x4 = 0 Solving 6 + -50x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -50x2 + -6 + x4 = 0 + -6 Reorder the terms: 6 + -6 + -50x2 + x4 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -50x2 + x4 = 0 + -6 -50x2 + x4 = 0 + -6 Combine like terms: 0 + -6 = -6 -50x2 + x4 = -6 The x term is -50x2. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x2 + 625 + x4 = -6 + 625 Reorder the terms: 625 + -50x2 + x4 = -6 + 625 Combine like terms: -6 + 625 = 619 625 + -50x2 + x4 = 619 Factor a perfect square on the left side: (x2 + -25)(x2 + -25) = 619 Calculate the square root of the right side: 24.879710609 Break this problem into two subproblems by setting (x2 + -25) equal to 24.879710609 and -24.879710609.Subproblem 1
x2 + -25 = 24.879710609 Simplifying x2 + -25 = 24.879710609 Reorder the terms: -25 + x2 = 24.879710609 Solving -25 + x2 = 24.879710609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x2 = 24.879710609 + 25 Combine like terms: -25 + 25 = 0 0 + x2 = 24.879710609 + 25 x2 = 24.879710609 + 25 Combine like terms: 24.879710609 + 25 = 49.879710609 x2 = 49.879710609 Simplifying x2 = 49.879710609 Take the square root of each side: x = {-7.062556946, 7.062556946}Subproblem 2
x2 + -25 = -24.879710609 Simplifying x2 + -25 = -24.879710609 Reorder the terms: -25 + x2 = -24.879710609 Solving -25 + x2 = -24.879710609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x2 = -24.879710609 + 25 Combine like terms: -25 + 25 = 0 0 + x2 = -24.879710609 + 25 x2 = -24.879710609 + 25 Combine like terms: -24.879710609 + 25 = 0.120289391 x2 = 0.120289391 Simplifying x2 = 0.120289391 Take the square root of each side: x = {-0.34682761, 0.34682761}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-7.062556946, 7.062556946, -0.34682761, 0.34682761}
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