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Simplifying 2x4 + 7x2 + -12 = 0 Reorder the terms: -12 + 7x2 + 2x4 = 0 Solving -12 + 7x2 + 2x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -6 + 3.5x2 + x4 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 3.5x2 + 6 + x4 = 0 + 6 Reorder the terms: -6 + 6 + 3.5x2 + x4 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 3.5x2 + x4 = 0 + 6 3.5x2 + x4 = 0 + 6 Combine like terms: 0 + 6 = 6 3.5x2 + x4 = 6 The x term is 3.5x2. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x2 + 3.0625 + x4 = 6 + 3.0625 Reorder the terms: 3.0625 + 3.5x2 + x4 = 6 + 3.0625 Combine like terms: 6 + 3.0625 = 9.0625 3.0625 + 3.5x2 + x4 = 9.0625 Factor a perfect square on the left side: (x2 + 1.75)(x2 + 1.75) = 9.0625 Calculate the square root of the right side: 3.010398645 Break this problem into two subproblems by setting (x2 + 1.75) equal to 3.010398645 and -3.010398645.Subproblem 1
x2 + 1.75 = 3.010398645 Simplifying x2 + 1.75 = 3.010398645 Reorder the terms: 1.75 + x2 = 3.010398645 Solving 1.75 + x2 = 3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x2 = 3.010398645 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x2 = 3.010398645 + -1.75 x2 = 3.010398645 + -1.75 Combine like terms: 3.010398645 + -1.75 = 1.260398645 x2 = 1.260398645 Simplifying x2 = 1.260398645 Take the square root of each side: x = {-1.122674773, 1.122674773}Subproblem 2
x2 + 1.75 = -3.010398645 Simplifying x2 + 1.75 = -3.010398645 Reorder the terms: 1.75 + x2 = -3.010398645 Solving 1.75 + x2 = -3.010398645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x2 = -3.010398645 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x2 = -3.010398645 + -1.75 x2 = -3.010398645 + -1.75 Combine like terms: -3.010398645 + -1.75 = -4.760398645 x2 = -4.760398645 Simplifying x2 = -4.760398645 Reorder the terms: 4.760398645 + x2 = -4.760398645 + 4.760398645 Combine like terms: -4.760398645 + 4.760398645 = 0.000000000 4.760398645 + x2 = 0.000000000 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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