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Simplifying 14x4 + 3x2 + -28 = 0 Reorder the terms: -28 + 3x2 + 14x4 = 0 Solving -28 + 3x2 + 14x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -2 + 0.2142857143x2 + x4 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 0.2142857143x2 + 2 + x4 = 0 + 2 Reorder the terms: -2 + 2 + 0.2142857143x2 + x4 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 0.2142857143x2 + x4 = 0 + 2 0.2142857143x2 + x4 = 0 + 2 Combine like terms: 0 + 2 = 2 0.2142857143x2 + x4 = 2 The x term is 0.2142857143x2. Take half its coefficient (0.1071428572). Square it (0.01147959185) and add it to both sides. Add '0.01147959185' to each side of the equation. 0.2142857143x2 + 0.01147959185 + x4 = 2 + 0.01147959185 Reorder the terms: 0.01147959185 + 0.2142857143x2 + x4 = 2 + 0.01147959185 Combine like terms: 2 + 0.01147959185 = 2.01147959185 0.01147959185 + 0.2142857143x2 + x4 = 2.01147959185 Factor a perfect square on the left side: (x2 + 0.1071428572)(x2 + 0.1071428572) = 2.01147959185 Calculate the square root of the right side: 1.418266404 Break this problem into two subproblems by setting (x2 + 0.1071428572) equal to 1.418266404 and -1.418266404.Subproblem 1
x2 + 0.1071428572 = 1.418266404 Simplifying x2 + 0.1071428572 = 1.418266404 Reorder the terms: 0.1071428572 + x2 = 1.418266404 Solving 0.1071428572 + x2 = 1.418266404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1071428572' to each side of the equation. 0.1071428572 + -0.1071428572 + x2 = 1.418266404 + -0.1071428572 Combine like terms: 0.1071428572 + -0.1071428572 = 0.0000000000 0.0000000000 + x2 = 1.418266404 + -0.1071428572 x2 = 1.418266404 + -0.1071428572 Combine like terms: 1.418266404 + -0.1071428572 = 1.3111235468 x2 = 1.3111235468 Simplifying x2 = 1.3111235468 Take the square root of each side: x = {-1.145043033, 1.145043033}Subproblem 2
x2 + 0.1071428572 = -1.418266404 Simplifying x2 + 0.1071428572 = -1.418266404 Reorder the terms: 0.1071428572 + x2 = -1.418266404 Solving 0.1071428572 + x2 = -1.418266404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1071428572' to each side of the equation. 0.1071428572 + -0.1071428572 + x2 = -1.418266404 + -0.1071428572 Combine like terms: 0.1071428572 + -0.1071428572 = 0.0000000000 0.0000000000 + x2 = -1.418266404 + -0.1071428572 x2 = -1.418266404 + -0.1071428572 Combine like terms: -1.418266404 + -0.1071428572 = -1.5254092612 x2 = -1.5254092612 Simplifying x2 = -1.5254092612 Reorder the terms: 1.5254092612 + x2 = -1.5254092612 + 1.5254092612 Combine like terms: -1.5254092612 + 1.5254092612 = 0.0000000000 1.5254092612 + x2 = 0.0000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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