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Simplifying x4 + 3 = 8x2 Reorder the terms: 3 + x4 = 8x2 Solving 3 + x4 = 8x2 Solving for variable 'x'. Reorder the terms: 3 + -8x2 + x4 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 3 + -8x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -8x2 + -3 + x4 = 0 + -3 Reorder the terms: 3 + -3 + -8x2 + x4 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8x2 + x4 = 0 + -3 -8x2 + x4 = 0 + -3 Combine like terms: 0 + -3 = -3 -8x2 + x4 = -3 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 + 16 Reorder the terms: 16 + -8x2 + x4 = -3 + 16 Combine like terms: -3 + 16 = 13 16 + -8x2 + x4 = 13 Factor a perfect square on the left side: (x2 + -4)(x2 + -4) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x2 + -4) equal to 3.605551275 and -3.605551275.Subproblem 1
x2 + -4 = 3.605551275 Simplifying x2 + -4 = 3.605551275 Reorder the terms: -4 + x2 = 3.605551275 Solving -4 + x2 = 3.605551275 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 = 3.605551275 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = 3.605551275 + 4 x2 = 3.605551275 + 4 Combine like terms: 3.605551275 + 4 = 7.605551275 x2 = 7.605551275 Simplifying x2 = 7.605551275 Take the square root of each side: x = {-2.757816396, 2.757816396}Subproblem 2
x2 + -4 = -3.605551275 Simplifying x2 + -4 = -3.605551275 Reorder the terms: -4 + x2 = -3.605551275 Solving -4 + x2 = -3.605551275 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 = -3.605551275 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = -3.605551275 + 4 x2 = -3.605551275 + 4 Combine like terms: -3.605551275 + 4 = 0.394448725 x2 = 0.394448725 Simplifying x2 = 0.394448725 Take the square root of each side: x = {-0.628051531, 0.628051531}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.757816396, 2.757816396, -0.628051531, 0.628051531}
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