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Simplifying 25b4 + -80b2c2 + 64c4 = 0 Reorder the terms: -80b2c2 + 25b4 + 64c4 = 0 Solving -80b2c2 + 25b4 + 64c4 = 0 Solving for variable 'b'. Factor a trinomial. (5b2 + -8c2)(5b2 + -8c2) = 0Subproblem 1
Set the factor '(5b2 + -8c2)' equal to zero and attempt to solve: Simplifying 5b2 + -8c2 = 0 Solving 5b2 + -8c2 = 0 Move all terms containing b to the left, all other terms to the right. Add '8c2' to each side of the equation. 5b2 + -8c2 + 8c2 = 0 + 8c2 Combine like terms: -8c2 + 8c2 = 0 5b2 + 0 = 0 + 8c2 5b2 = 0 + 8c2 Remove the zero: 5b2 = 8c2 Divide each side by '5'. b2 = 1.6c2 Simplifying b2 = 1.6c2 Take the square root of each side: b = {-1.264911064c, 1.264911064c}Subproblem 2
Set the factor '(5b2 + -8c2)' equal to zero and attempt to solve: Simplifying 5b2 + -8c2 = 0 Solving 5b2 + -8c2 = 0 Move all terms containing b to the left, all other terms to the right. Add '8c2' to each side of the equation. 5b2 + -8c2 + 8c2 = 0 + 8c2 Combine like terms: -8c2 + 8c2 = 0 5b2 + 0 = 0 + 8c2 5b2 = 0 + 8c2 Remove the zero: 5b2 = 8c2 Divide each side by '5'. b2 = 1.6c2 Simplifying b2 = 1.6c2 Take the square root of each side: b = {-1.264911064c, 1.264911064c}Solution
b = {-1.264911064c, 1.264911064c, -1.264911064c, 1.264911064c}
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