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Simplifying x4 + -8x2 + 0.5 = -2 Reorder the terms: 0.5 + -8x2 + x4 = -2 Solving 0.5 + -8x2 + x4 = -2 Solving for variable 'x'. Reorder the terms: 0.5 + 2 + -8x2 + x4 = -2 + 2 Combine like terms: 0.5 + 2 = 2.5 2.5 + -8x2 + x4 = -2 + 2 Combine like terms: -2 + 2 = 0 2.5 + -8x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -8x2 + -2.5 + x4 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -8x2 + x4 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -8x2 + x4 = 0 + -2.5 -8x2 + x4 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -8x2 + x4 = -2.5 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 = -2.5 + 16 Reorder the terms: 16 + -8x2 + x4 = -2.5 + 16 Combine like terms: -2.5 + 16 = 13.5 16 + -8x2 + x4 = 13.5 Factor a perfect square on the left side: (x2 + -4)(x2 + -4) = 13.5 Calculate the square root of the right side: 3.674234614 Break this problem into two subproblems by setting (x2 + -4) equal to 3.674234614 and -3.674234614.Subproblem 1
x2 + -4 = 3.674234614 Simplifying x2 + -4 = 3.674234614 Reorder the terms: -4 + x2 = 3.674234614 Solving -4 + x2 = 3.674234614 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 = 3.674234614 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = 3.674234614 + 4 x2 = 3.674234614 + 4 Combine like terms: 3.674234614 + 4 = 7.674234614 x2 = 7.674234614 Simplifying x2 = 7.674234614 Take the square root of each side: x = {-2.770240895, 2.770240895}Subproblem 2
x2 + -4 = -3.674234614 Simplifying x2 + -4 = -3.674234614 Reorder the terms: -4 + x2 = -3.674234614 Solving -4 + x2 = -3.674234614 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 = -3.674234614 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = -3.674234614 + 4 x2 = -3.674234614 + 4 Combine like terms: -3.674234614 + 4 = 0.325765386 x2 = 0.325765386 Simplifying x2 = 0.325765386 Take the square root of each side: x = {-0.570758606, 0.570758606}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.770240895, 2.770240895, -0.570758606, 0.570758606}
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