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Simplifying (3x4 + 6x2 + -1) + -1(2x4 + -8x2 + 5) = 0 Reorder the terms: (-1 + 6x2 + 3x4) + -1(2x4 + -8x2 + 5) = 0 Remove parenthesis around (-1 + 6x2 + 3x4) -1 + 6x2 + 3x4 + -1(2x4 + -8x2 + 5) = 0 Reorder the terms: -1 + 6x2 + 3x4 + -1(5 + -8x2 + 2x4) = 0 -1 + 6x2 + 3x4 + (5 * -1 + -8x2 * -1 + 2x4 * -1) = 0 -1 + 6x2 + 3x4 + (-5 + 8x2 + -2x4) = 0 Reorder the terms: -1 + -5 + 6x2 + 8x2 + 3x4 + -2x4 = 0 Combine like terms: -1 + -5 = -6 -6 + 6x2 + 8x2 + 3x4 + -2x4 = 0 Combine like terms: 6x2 + 8x2 = 14x2 -6 + 14x2 + 3x4 + -2x4 = 0 Combine like terms: 3x4 + -2x4 = 1x4 -6 + 14x2 + 1x4 = 0 Solving -6 + 14x2 + 1x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + 14x2 + 6 + x4 = 0 + 6 Reorder the terms: -6 + 6 + 14x2 + x4 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 14x2 + x4 = 0 + 6 14x2 + x4 = 0 + 6 Combine like terms: 0 + 6 = 6 14x2 + x4 = 6 The x term is 14x2. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14x2 + 49 + x4 = 6 + 49 Reorder the terms: 49 + 14x2 + x4 = 6 + 49 Combine like terms: 6 + 49 = 55 49 + 14x2 + x4 = 55 Factor a perfect square on the left side: (x2 + 7)(x2 + 7) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (x2 + 7) equal to 7.416198487 and -7.416198487.Subproblem 1
x2 + 7 = 7.416198487 Simplifying x2 + 7 = 7.416198487 Reorder the terms: 7 + x2 = 7.416198487 Solving 7 + x2 = 7.416198487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x2 = 7.416198487 + -7 Combine like terms: 7 + -7 = 0 0 + x2 = 7.416198487 + -7 x2 = 7.416198487 + -7 Combine like terms: 7.416198487 + -7 = 0.416198487 x2 = 0.416198487 Simplifying x2 = 0.416198487 Take the square root of each side: x = {-0.645134472, 0.645134472}Subproblem 2
x2 + 7 = -7.416198487 Simplifying x2 + 7 = -7.416198487 Reorder the terms: 7 + x2 = -7.416198487 Solving 7 + x2 = -7.416198487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x2 = -7.416198487 + -7 Combine like terms: 7 + -7 = 0 0 + x2 = -7.416198487 + -7 x2 = -7.416198487 + -7 Combine like terms: -7.416198487 + -7 = -14.416198487 x2 = -14.416198487 Simplifying x2 = -14.416198487 Reorder the terms: 14.416198487 + x2 = -14.416198487 + 14.416198487 Combine like terms: -14.416198487 + 14.416198487 = 0.000000000 14.416198487 + 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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