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Simplifying (4x4 + 1) + -1(3x4 + 6x2 + -5) = 0 Reorder the terms: (1 + 4x4) + -1(3x4 + 6x2 + -5) = 0 Remove parenthesis around (1 + 4x4) 1 + 4x4 + -1(3x4 + 6x2 + -5) = 0 Reorder the terms: 1 + 4x4 + -1(-5 + 6x2 + 3x4) = 0 1 + 4x4 + (-5 * -1 + 6x2 * -1 + 3x4 * -1) = 0 1 + 4x4 + (5 + -6x2 + -3x4) = 0 Reorder the terms: 1 + 5 + -6x2 + 4x4 + -3x4 = 0 Combine like terms: 1 + 5 = 6 6 + -6x2 + 4x4 + -3x4 = 0 Combine like terms: 4x4 + -3x4 = 1x4 6 + -6x2 + 1x4 = 0 Solving 6 + -6x2 + 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 + -6x2 + -6 + x4 = 0 + -6 Reorder the terms: 6 + -6 + -6x2 + x4 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -6x2 + x4 = 0 + -6 -6x2 + x4 = 0 + -6 Combine like terms: 0 + -6 = -6 -6x2 + x4 = -6 The x term is -6x2. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x2 + 9 + x4 = -6 + 9 Reorder the terms: 9 + -6x2 + x4 = -6 + 9 Combine like terms: -6 + 9 = 3 9 + -6x2 + x4 = 3 Factor a perfect square on the left side: (x2 + -3)(x2 + -3) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x2 + -3) equal to 1.732050808 and -1.732050808.Subproblem 1
x2 + -3 = 1.732050808 Simplifying x2 + -3 = 1.732050808 Reorder the terms: -3 + x2 = 1.732050808 Solving -3 + x2 = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x2 = 1.732050808 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = 1.732050808 + 3 x2 = 1.732050808 + 3 Combine like terms: 1.732050808 + 3 = 4.732050808 x2 = 4.732050808 Simplifying x2 = 4.732050808 Take the square root of each side: x = {-2.175327747, 2.175327747}Subproblem 2
x2 + -3 = -1.732050808 Simplifying x2 + -3 = -1.732050808 Reorder the terms: -3 + x2 = -1.732050808 Solving -3 + x2 = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x2 = -1.732050808 + 3 Combine like terms: -3 + 3 = 0 0 + x2 = -1.732050808 + 3 x2 = -1.732050808 + 3 Combine like terms: -1.732050808 + 3 = 1.267949192 x2 = 1.267949192 Simplifying x2 = 1.267949192 Take the square root of each side: x = {-1.1260325, 1.1260325}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.175327747, 2.175327747, -1.1260325, 1.1260325}
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