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Simplifying x4 + -14x2 + 25 = 0 Reorder the terms: 25 + -14x2 + x4 = 0 Solving 25 + -14x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -14x2 + -25 + x4 = 0 + -25 Reorder the terms: 25 + -25 + -14x2 + x4 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -14x2 + x4 = 0 + -25 -14x2 + x4 = 0 + -25 Combine like terms: 0 + -25 = -25 -14x2 + x4 = -25 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 = -25 + 49 Reorder the terms: 49 + -14x2 + x4 = -25 + 49 Combine like terms: -25 + 49 = 24 49 + -14x2 + x4 = 24 Factor a perfect square on the left side: (x2 + -7)(x2 + -7) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (x2 + -7) equal to 4.898979486 and -4.898979486.Subproblem 1
x2 + -7 = 4.898979486 Simplifying x2 + -7 = 4.898979486 Reorder the terms: -7 + x2 = 4.898979486 Solving -7 + x2 = 4.898979486 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 = 4.898979486 + 7 Combine like terms: -7 + 7 = 0 0 + x2 = 4.898979486 + 7 x2 = 4.898979486 + 7 Combine like terms: 4.898979486 + 7 = 11.898979486 x2 = 11.898979486 Simplifying x2 = 11.898979486 Take the square root of each side: x = {-3.449489743, 3.449489743}Subproblem 2
x2 + -7 = -4.898979486 Simplifying x2 + -7 = -4.898979486 Reorder the terms: -7 + x2 = -4.898979486 Solving -7 + x2 = -4.898979486 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 = -4.898979486 + 7 Combine like terms: -7 + 7 = 0 0 + x2 = -4.898979486 + 7 x2 = -4.898979486 + 7 Combine like terms: -4.898979486 + 7 = 2.101020514 x2 = 2.101020514 Simplifying x2 = 2.101020514 Take the square root of each side: x = {-1.449489743, 1.449489743}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.449489743, 3.449489743, -1.449489743, 1.449489743}
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