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Simplifying x4 + -3.24x2 + -52 = 0 Reorder the terms: -52 + -3.24x2 + x4 = 0 Solving -52 + -3.24x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + -3.24x2 + 52 + x4 = 0 + 52 Reorder the terms: -52 + 52 + -3.24x2 + x4 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + -3.24x2 + x4 = 0 + 52 -3.24x2 + x4 = 0 + 52 Combine like terms: 0 + 52 = 52 -3.24x2 + x4 = 52 The x term is -3.24x2. Take half its coefficient (-1.62). Square it (2.6244) and add it to both sides. Add '2.6244' to each side of the equation. -3.24x2 + 2.6244 + x4 = 52 + 2.6244 Reorder the terms: 2.6244 + -3.24x2 + x4 = 52 + 2.6244 Combine like terms: 52 + 2.6244 = 54.6244 2.6244 + -3.24x2 + x4 = 54.6244 Factor a perfect square on the left side: (x2 + -1.62)(x2 + -1.62) = 54.6244 Calculate the square root of the right side: 7.390832159 Break this problem into two subproblems by setting (x2 + -1.62) equal to 7.390832159 and -7.390832159.Subproblem 1
x2 + -1.62 = 7.390832159 Simplifying x2 + -1.62 = 7.390832159 Reorder the terms: -1.62 + x2 = 7.390832159 Solving -1.62 + x2 = 7.390832159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.62' to each side of the equation. -1.62 + 1.62 + x2 = 7.390832159 + 1.62 Combine like terms: -1.62 + 1.62 = 0.00 0.00 + x2 = 7.390832159 + 1.62 x2 = 7.390832159 + 1.62 Combine like terms: 7.390832159 + 1.62 = 9.010832159 x2 = 9.010832159 Simplifying x2 = 9.010832159 Take the square root of each side: x = {-3.001804817, 3.001804817}Subproblem 2
x2 + -1.62 = -7.390832159 Simplifying x2 + -1.62 = -7.390832159 Reorder the terms: -1.62 + x2 = -7.390832159 Solving -1.62 + x2 = -7.390832159 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.62' to each side of the equation. -1.62 + 1.62 + x2 = -7.390832159 + 1.62 Combine like terms: -1.62 + 1.62 = 0.00 0.00 + x2 = -7.390832159 + 1.62 x2 = -7.390832159 + 1.62 Combine like terms: -7.390832159 + 1.62 = -5.770832159 x2 = -5.770832159 Simplifying x2 = -5.770832159 Reorder the terms: 5.770832159 + x2 = -5.770832159 + 5.770832159 Combine like terms: -5.770832159 + 5.770832159 = 0.000000000 5.770832159 + 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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