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Simplifying x4 + -8x2 = 7 Reorder the terms: -8x2 + x4 = 7 Solving -8x2 + x4 = 7 Solving for variable 'x'. Reorder the terms: -7 + -8x2 + x4 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + -8x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -8x2 + 7 + x4 = 0 + 7 Reorder the terms: -7 + 7 + -8x2 + x4 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -8x2 + x4 = 0 + 7 -8x2 + x4 = 0 + 7 Combine like terms: 0 + 7 = 7 -8x2 + x4 = 7 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 = 7 + 16 Reorder the terms: 16 + -8x2 + x4 = 7 + 16 Combine like terms: 7 + 16 = 23 16 + -8x2 + x4 = 23 Factor a perfect square on the left side: (x2 + -4)(x2 + -4) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (x2 + -4) equal to 4.795831523 and -4.795831523.Subproblem 1
x2 + -4 = 4.795831523 Simplifying x2 + -4 = 4.795831523 Reorder the terms: -4 + x2 = 4.795831523 Solving -4 + x2 = 4.795831523 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 = 4.795831523 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = 4.795831523 + 4 x2 = 4.795831523 + 4 Combine like terms: 4.795831523 + 4 = 8.795831523 x2 = 8.795831523 Simplifying x2 = 8.795831523 Take the square root of each side: x = {-2.965776715, 2.965776715}Subproblem 2
x2 + -4 = -4.795831523 Simplifying x2 + -4 = -4.795831523 Reorder the terms: -4 + x2 = -4.795831523 Solving -4 + x2 = -4.795831523 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 = -4.795831523 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = -4.795831523 + 4 x2 = -4.795831523 + 4 Combine like terms: -4.795831523 + 4 = -0.795831523 x2 = -0.795831523 Simplifying x2 = -0.795831523 Reorder the terms: 0.795831523 + x2 = -0.795831523 + 0.795831523 Combine like terms: -0.795831523 + 0.795831523 = 0.000000000 0.795831523 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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