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Simplifying x4 + 32 + -14x2 = 0 Reorder the terms: 32 + -14x2 + x4 = 0 Solving 32 + -14x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-32' to each side of the equation. 32 + -14x2 + -32 + x4 = 0 + -32 Reorder the terms: 32 + -32 + -14x2 + x4 = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -14x2 + x4 = 0 + -32 -14x2 + x4 = 0 + -32 Combine like terms: 0 + -32 = -32 -14x2 + x4 = -32 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 = -32 + 49 Reorder the terms: 49 + -14x2 + x4 = -32 + 49 Combine like terms: -32 + 49 = 17 49 + -14x2 + x4 = 17 Factor a perfect square on the left side: (x2 + -7)(x2 + -7) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (x2 + -7) equal to 4.123105626 and -4.123105626.Subproblem 1
x2 + -7 = 4.123105626 Simplifying x2 + -7 = 4.123105626 Reorder the terms: -7 + x2 = 4.123105626 Solving -7 + x2 = 4.123105626 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 = 4.123105626 + 7 Combine like terms: -7 + 7 = 0 0 + x2 = 4.123105626 + 7 x2 = 4.123105626 + 7 Combine like terms: 4.123105626 + 7 = 11.123105626 x2 = 11.123105626 Simplifying x2 = 11.123105626 Take the square root of each side: x = {-3.335132025, 3.335132025}Subproblem 2
x2 + -7 = -4.123105626 Simplifying x2 + -7 = -4.123105626 Reorder the terms: -7 + x2 = -4.123105626 Solving -7 + x2 = -4.123105626 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 = -4.123105626 + 7 Combine like terms: -7 + 7 = 0 0 + x2 = -4.123105626 + 7 x2 = -4.123105626 + 7 Combine like terms: -4.123105626 + 7 = 2.876894374 x2 = 2.876894374 Simplifying x2 = 2.876894374 Take the square root of each side: x = {-1.696141024, 1.696141024}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.335132025, 3.335132025, -1.696141024, 1.696141024}
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