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Simplifying 2x4 = 16x2 + -23 Reorder the terms: 2x4 = -23 + 16x2 Solving 2x4 = -23 + 16x2 Solving for variable 'x'. Reorder the terms: 23 + -16x2 + 2x4 = -23 + 16x2 + 23 + -16x2 Reorder the terms: 23 + -16x2 + 2x4 = -23 + 23 + 16x2 + -16x2 Combine like terms: -23 + 23 = 0 23 + -16x2 + 2x4 = 0 + 16x2 + -16x2 23 + -16x2 + 2x4 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 23 + -16x2 + 2x4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 11.5 + -8x2 + x4 = 0 Move the constant term to the right: Add '-11.5' to each side of the equation. 11.5 + -8x2 + -11.5 + x4 = 0 + -11.5 Reorder the terms: 11.5 + -11.5 + -8x2 + x4 = 0 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + -8x2 + x4 = 0 + -11.5 -8x2 + x4 = 0 + -11.5 Combine like terms: 0 + -11.5 = -11.5 -8x2 + x4 = -11.5 The x term is -8x2. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x2 + 16 + x4 = -11.5 + 16 Reorder the terms: 16 + -8x2 + x4 = -11.5 + 16 Combine like terms: -11.5 + 16 = 4.5 16 + -8x2 + x4 = 4.5 Factor a perfect square on the left side: (x2 + -4)(x2 + -4) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (x2 + -4) equal to 2.121320344 and -2.121320344.Subproblem 1
x2 + -4 = 2.121320344 Simplifying x2 + -4 = 2.121320344 Reorder the terms: -4 + x2 = 2.121320344 Solving -4 + x2 = 2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = 2.121320344 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = 2.121320344 + 4 x2 = 2.121320344 + 4 Combine like terms: 2.121320344 + 4 = 6.121320344 x2 = 6.121320344 Simplifying x2 = 6.121320344 Take the square root of each side: x = {-2.47413022, 2.47413022}Subproblem 2
x2 + -4 = -2.121320344 Simplifying x2 + -4 = -2.121320344 Reorder the terms: -4 + x2 = -2.121320344 Solving -4 + x2 = -2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = -2.121320344 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = -2.121320344 + 4 x2 = -2.121320344 + 4 Combine like terms: -2.121320344 + 4 = 1.878679656 x2 = 1.878679656 Simplifying x2 = 1.878679656 Take the square root of each side: x = {-1.370649356, 1.370649356}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.47413022, 2.47413022, -1.370649356, 1.370649356}
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