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Simplifying 22x2 + -75 = x4 Reorder the terms: -75 + 22x2 = x4 Solving -75 + 22x2 = x4 Solving for variable 'x'. Combine like terms: x4 + -1x4 = 0 -75 + 22x2 + -1x4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 75 + -22x2 + x4 = 0 Move the constant term to the right: Add '-75' to each side of the equation. 75 + -22x2 + -75 + x4 = 0 + -75 Reorder the terms: 75 + -75 + -22x2 + x4 = 0 + -75 Combine like terms: 75 + -75 = 0 0 + -22x2 + x4 = 0 + -75 -22x2 + x4 = 0 + -75 Combine like terms: 0 + -75 = -75 -22x2 + x4 = -75 The x term is -22x2. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x2 + 121 + x4 = -75 + 121 Reorder the terms: 121 + -22x2 + x4 = -75 + 121 Combine like terms: -75 + 121 = 46 121 + -22x2 + x4 = 46 Factor a perfect square on the left side: (x2 + -11)(x2 + -11) = 46 Calculate the square root of the right side: 6.782329983 Break this problem into two subproblems by setting (x2 + -11) equal to 6.782329983 and -6.782329983.Subproblem 1
x2 + -11 = 6.782329983 Simplifying x2 + -11 = 6.782329983 Reorder the terms: -11 + x2 = 6.782329983 Solving -11 + x2 = 6.782329983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x2 = 6.782329983 + 11 Combine like terms: -11 + 11 = 0 0 + x2 = 6.782329983 + 11 x2 = 6.782329983 + 11 Combine like terms: 6.782329983 + 11 = 17.782329983 x2 = 17.782329983 Simplifying x2 = 17.782329983 Take the square root of each side: x = {-4.216910004, 4.216910004}Subproblem 2
x2 + -11 = -6.782329983 Simplifying x2 + -11 = -6.782329983 Reorder the terms: -11 + x2 = -6.782329983 Solving -11 + x2 = -6.782329983 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x2 = -6.782329983 + 11 Combine like terms: -11 + 11 = 0 0 + x2 = -6.782329983 + 11 x2 = -6.782329983 + 11 Combine like terms: -6.782329983 + 11 = 4.217670017 x2 = 4.217670017 Simplifying x2 = 4.217670017 Take the square root of each side: x = {-2.053696671, 2.053696671}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.216910004, 4.216910004, -2.053696671, 2.053696671}
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