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Simplifying x4 + -15x2 + 9 = 0 Reorder the terms: 9 + -15x2 + x4 = 0 Solving 9 + -15x2 + 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 + -15x2 + -9 + x4 = 0 + -9 Reorder the terms: 9 + -9 + -15x2 + x4 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -15x2 + x4 = 0 + -9 -15x2 + x4 = 0 + -9 Combine like terms: 0 + -9 = -9 -15x2 + x4 = -9 The x term is -15x2. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x2 + 56.25 + x4 = -9 + 56.25 Reorder the terms: 56.25 + -15x2 + x4 = -9 + 56.25 Combine like terms: -9 + 56.25 = 47.25 56.25 + -15x2 + x4 = 47.25 Factor a perfect square on the left side: (x2 + -7.5)(x2 + -7.5) = 47.25 Calculate the square root of the right side: 6.873863542 Break this problem into two subproblems by setting (x2 + -7.5) equal to 6.873863542 and -6.873863542.Subproblem 1
x2 + -7.5 = 6.873863542 Simplifying x2 + -7.5 = 6.873863542 Reorder the terms: -7.5 + x2 = 6.873863542 Solving -7.5 + x2 = 6.873863542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x2 = 6.873863542 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x2 = 6.873863542 + 7.5 x2 = 6.873863542 + 7.5 Combine like terms: 6.873863542 + 7.5 = 14.373863542 x2 = 14.373863542 Simplifying x2 = 14.373863542 Take the square root of each side: x = {-3.791287847, 3.791287847}Subproblem 2
x2 + -7.5 = -6.873863542 Simplifying x2 + -7.5 = -6.873863542 Reorder the terms: -7.5 + x2 = -6.873863542 Solving -7.5 + x2 = -6.873863542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x2 = -6.873863542 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x2 = -6.873863542 + 7.5 x2 = -6.873863542 + 7.5 Combine like terms: -6.873863542 + 7.5 = 0.626136458 x2 = 0.626136458 Simplifying x2 = 0.626136458 Take the square root of each side: x = {-0.791287848, 0.791287848}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.791287847, 3.791287847, -0.791287848, 0.791287848}
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