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Simplifying x2(x2) + -16(x2 + -1) = 0 Multiply x2 * x2 x4 + -16(x2 + -1) = 0 Reorder the terms: x4 + -16(-1 + x2) = 0 x4 + (-1 * -16 + x2 * -16) = 0 x4 + (16 + -16x2) = 0 Reorder the terms: 16 + -16x2 + x4 = 0 Solving 16 + -16x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + -16x2 + -16 + x4 = 0 + -16 Reorder the terms: 16 + -16 + -16x2 + x4 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -16x2 + x4 = 0 + -16 -16x2 + x4 = 0 + -16 Combine like terms: 0 + -16 = -16 -16x2 + x4 = -16 The x term is -16x2. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x2 + 64 + x4 = -16 + 64 Reorder the terms: 64 + -16x2 + x4 = -16 + 64 Combine like terms: -16 + 64 = 48 64 + -16x2 + x4 = 48 Factor a perfect square on the left side: (x2 + -8)(x2 + -8) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x2 + -8) equal to 6.92820323 and -6.92820323.Subproblem 1
x2 + -8 = 6.92820323 Simplifying x2 + -8 = 6.92820323 Reorder the terms: -8 + x2 = 6.92820323 Solving -8 + x2 = 6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x2 = 6.92820323 + 8 Combine like terms: -8 + 8 = 0 0 + x2 = 6.92820323 + 8 x2 = 6.92820323 + 8 Combine like terms: 6.92820323 + 8 = 14.92820323 x2 = 14.92820323 Simplifying x2 = 14.92820323 Take the square root of each side: x = {-3.863703305, 3.863703305}Subproblem 2
x2 + -8 = -6.92820323 Simplifying x2 + -8 = -6.92820323 Reorder the terms: -8 + x2 = -6.92820323 Solving -8 + x2 = -6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x2 = -6.92820323 + 8 Combine like terms: -8 + 8 = 0 0 + x2 = -6.92820323 + 8 x2 = -6.92820323 + 8 Combine like terms: -6.92820323 + 8 = 1.07179677 x2 = 1.07179677 Simplifying x2 = 1.07179677 Take the square root of each side: x = {-1.035276181, 1.035276181}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.863703305, 3.863703305, -1.035276181, 1.035276181}
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