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Simplifying x4 + 3x2 + -7 = 0 Reorder the terms: -7 + 3x2 + x4 = 0 Solving -7 + 3x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 3x2 + 7 + x4 = 0 + 7 Reorder the terms: -7 + 7 + 3x2 + x4 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 3x2 + x4 = 0 + 7 3x2 + x4 = 0 + 7 Combine like terms: 0 + 7 = 7 3x2 + x4 = 7 The x term is 3x2. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x2 + 2.25 + x4 = 7 + 2.25 Reorder the terms: 2.25 + 3x2 + x4 = 7 + 2.25 Combine like terms: 7 + 2.25 = 9.25 2.25 + 3x2 + x4 = 9.25 Factor a perfect square on the left side: (x2 + 1.5)(x2 + 1.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (x2 + 1.5) equal to 3.041381265 and -3.041381265.Subproblem 1
x2 + 1.5 = 3.041381265 Simplifying x2 + 1.5 = 3.041381265 Reorder the terms: 1.5 + x2 = 3.041381265 Solving 1.5 + x2 = 3.041381265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x2 = 3.041381265 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x2 = 3.041381265 + -1.5 x2 = 3.041381265 + -1.5 Combine like terms: 3.041381265 + -1.5 = 1.541381265 x2 = 1.541381265 Simplifying x2 = 1.541381265 Take the square root of each side: x = {-1.241523767, 1.241523767}Subproblem 2
x2 + 1.5 = -3.041381265 Simplifying x2 + 1.5 = -3.041381265 Reorder the terms: 1.5 + x2 = -3.041381265 Solving 1.5 + x2 = -3.041381265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x2 = -3.041381265 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x2 = -3.041381265 + -1.5 x2 = -3.041381265 + -1.5 Combine like terms: -3.041381265 + -1.5 = -4.541381265 x2 = -4.541381265 Simplifying x2 = -4.541381265 Reorder the terms: 4.541381265 + x2 = -4.541381265 + 4.541381265 Combine like terms: -4.541381265 + 4.541381265 = 0.000000000 4.541381265 + 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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