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Simplifying 81x8 + -97b4x4 + 16b8 = 0 Reorder the terms: -97b4x4 + 16b8 + 81x8 = 0 Solving -97b4x4 + 16b8 + 81x8 = 0 Solving for variable 'b'. Factor a trinomial. (16b4 + -81x4)(b4 + -1x4) = 0 Factor a difference between two squares. ((4b2 + 9x2)(4b2 + -9x2))(b4 + -1x4) = 0 Factor a difference between two squares. ((4b2 + 9x2)((2b + 3x)(2b + -3x)))(b4 + -1x4) = 0 Factor a difference between two squares. ((b2 + x2)(b2 + -1x2))(4b2 + 9x2)(2b + 3x)(2b + -3x) = 0 Factor a difference between two squares. ((b2 + x2)((b + x)(b + -1x)))(4b2 + 9x2)(2b + 3x)(2b + -3x) = 0Subproblem 1
Set the factor '(4b2 + 9x2)' equal to zero and attempt to solve: Simplifying 4b2 + 9x2 = 0 Solving 4b2 + 9x2 = 0 Move all terms containing b to the left, all other terms to the right. Add '-9x2' to each side of the equation. 4b2 + 9x2 + -9x2 = 0 + -9x2 Combine like terms: 9x2 + -9x2 = 0 4b2 + 0 = 0 + -9x2 4b2 = 0 + -9x2 Remove the zero: 4b2 = -9x2 Divide each side by '4'. b2 = -2.25x2 Simplifying b2 = -2.25x2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(2b + 3x)' equal to zero and attempt to solve: Simplifying 2b + 3x = 0 Solving 2b + 3x = 0 Move all terms containing b to the left, all other terms to the right. Add '-3x' to each side of the equation. 2b + 3x + -3x = 0 + -3x Combine like terms: 3x + -3x = 0 2b + 0 = 0 + -3x 2b = 0 + -3x Remove the zero: 2b = -3x Divide each side by '2'. b = -1.5x Simplifying b = -1.5xSubproblem 3
Set the factor '(2b + -3x)' equal to zero and attempt to solve: Simplifying 2b + -3x = 0 Solving 2b + -3x = 0 Move all terms containing b to the left, all other terms to the right. Add '3x' to each side of the equation. 2b + -3x + 3x = 0 + 3x Combine like terms: -3x + 3x = 0 2b + 0 = 0 + 3x 2b = 0 + 3x Remove the zero: 2b = 3x Divide each side by '2'. b = 1.5x Simplifying b = 1.5xSubproblem 4
Set the factor '(b2 + x2)' equal to zero and attempt to solve: Simplifying b2 + x2 = 0 Solving b2 + x2 = 0 Move all terms containing b to the left, all other terms to the right. Add '-1x2' to each side of the equation. b2 + x2 + -1x2 = 0 + -1x2 Combine like terms: x2 + -1x2 = 0 b2 + 0 = 0 + -1x2 b2 = 0 + -1x2 Remove the zero: b2 = -1x2 Simplifying b2 = -1x2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 5
Set the factor '(b + x)' equal to zero and attempt to solve: Simplifying b + x = 0 Solving b + x = 0 Move all terms containing b to the left, all other terms to the right. Add '-1x' to each side of the equation. b + x + -1x = 0 + -1x Combine like terms: x + -1x = 0 b + 0 = 0 + -1x b = 0 + -1x Remove the zero: b = -1x Simplifying b = -1xSubproblem 6
Set the factor '(b + -1x)' equal to zero and attempt to solve: Simplifying b + -1x = 0 Solving b + -1x = 0 Move all terms containing b to the left, all other terms to the right. Add 'x' to each side of the equation. b + -1x + x = 0 + x Combine like terms: -1x + x = 0 b + 0 = 0 + x b = 0 + x Remove the zero: b = x Simplifying b = xSolution
b = {-1.5x, 1.5x, -1x, x}
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