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Simplifying x4 + -7x2 + 9 = 0 Reorder the terms: 9 + -7x2 + x4 = 0 Solving 9 + -7x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -7x2 + -9 + x4 = 0 + -9 Reorder the terms: 9 + -9 + -7x2 + x4 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -7x2 + x4 = 0 + -9 -7x2 + x4 = 0 + -9 Combine like terms: 0 + -9 = -9 -7x2 + x4 = -9 The x term is -7x2. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x2 + 12.25 + x4 = -9 + 12.25 Reorder the terms: 12.25 + -7x2 + x4 = -9 + 12.25 Combine like terms: -9 + 12.25 = 3.25 12.25 + -7x2 + x4 = 3.25 Factor a perfect square on the left side: (x2 + -3.5)(x2 + -3.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (x2 + -3.5) equal to 1.802775638 and -1.802775638.Subproblem 1
x2 + -3.5 = 1.802775638 Simplifying x2 + -3.5 = 1.802775638 Reorder the terms: -3.5 + x2 = 1.802775638 Solving -3.5 + x2 = 1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x2 = 1.802775638 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x2 = 1.802775638 + 3.5 x2 = 1.802775638 + 3.5 Combine like terms: 1.802775638 + 3.5 = 5.302775638 x2 = 5.302775638 Simplifying x2 = 5.302775638 Take the square root of each side: x = {-2.302775638, 2.302775638}Subproblem 2
x2 + -3.5 = -1.802775638 Simplifying x2 + -3.5 = -1.802775638 Reorder the terms: -3.5 + x2 = -1.802775638 Solving -3.5 + x2 = -1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x2 = -1.802775638 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x2 = -1.802775638 + 3.5 x2 = -1.802775638 + 3.5 Combine like terms: -1.802775638 + 3.5 = 1.697224362 x2 = 1.697224362 Simplifying x2 = 1.697224362 Take the square root of each side: x = {-1.302775638, 1.302775638}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.302775638, 2.302775638, -1.302775638, 1.302775638}
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