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Simplifying 4x4 + -32x2 + 13 = 0 Reorder the terms: 13 + -32x2 + 4x4 = 0 Solving 13 + -32x2 + 4x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.25 + -8x2 + x4 = 0 Move the constant term to the right: Add '-3.25' to each side of the equation. 3.25 + -8x2 + -3.25 + x4 = 0 + -3.25 Reorder the terms: 3.25 + -3.25 + -8x2 + x4 = 0 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + -8x2 + x4 = 0 + -3.25 -8x2 + x4 = 0 + -3.25 Combine like terms: 0 + -3.25 = -3.25 -8x2 + x4 = -3.25 The x term is -8x2. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x2 + 16 + x4 = -3.25 + 16 Reorder the terms: 16 + -8x2 + x4 = -3.25 + 16 Combine like terms: -3.25 + 16 = 12.75 16 + -8x2 + x4 = 12.75 Factor a perfect square on the left side: (x2 + -4)(x2 + -4) = 12.75 Calculate the square root of the right side: 3.570714214 Break this problem into two subproblems by setting (x2 + -4) equal to 3.570714214 and -3.570714214.Subproblem 1
x2 + -4 = 3.570714214 Simplifying x2 + -4 = 3.570714214 Reorder the terms: -4 + x2 = 3.570714214 Solving -4 + x2 = 3.570714214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = 3.570714214 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = 3.570714214 + 4 x2 = 3.570714214 + 4 Combine like terms: 3.570714214 + 4 = 7.570714214 x2 = 7.570714214 Simplifying x2 = 7.570714214 Take the square root of each side: x = {-2.751493088, 2.751493088}Subproblem 2
x2 + -4 = -3.570714214 Simplifying x2 + -4 = -3.570714214 Reorder the terms: -4 + x2 = -3.570714214 Solving -4 + x2 = -3.570714214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = -3.570714214 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = -3.570714214 + 4 x2 = -3.570714214 + 4 Combine like terms: -3.570714214 + 4 = 0.429285786 x2 = 0.429285786 Simplifying x2 = 0.429285786 Take the square root of each side: x = {-0.655199043, 0.655199043}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.751493088, 2.751493088, -0.655199043, 0.655199043}
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