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Simplifying 89bx = 42x2 + 22b2 Reorder the terms: 89bx = 22b2 + 42x2 Solving 89bx = 22b2 + 42x2 Solving for variable 'b'. Reorder the terms: 89bx + -22b2 + -42x2 = 22b2 + -22b2 + 42x2 + -42x2 Combine like terms: 22b2 + -22b2 = 0 89bx + -22b2 + -42x2 = 0 + 42x2 + -42x2 89bx + -22b2 + -42x2 = 42x2 + -42x2 Combine like terms: 42x2 + -42x2 = 0 89bx + -22b2 + -42x2 = 0 Factor a trinomial. (-11b + 6x)(2b + -7x) = 0Subproblem 1
Set the factor '(-11b + 6x)' equal to zero and attempt to solve: Simplifying -11b + 6x = 0 Solving -11b + 6x = 0 Move all terms containing b to the left, all other terms to the right. Add '-6x' to each side of the equation. -11b + 6x + -6x = 0 + -6x Combine like terms: 6x + -6x = 0 -11b + 0 = 0 + -6x -11b = 0 + -6x Remove the zero: -11b = -6x Divide each side by '-11'. b = 0.5454545455x Simplifying b = 0.5454545455xSubproblem 2
Set the factor '(2b + -7x)' equal to zero and attempt to solve: Simplifying 2b + -7x = 0 Solving 2b + -7x = 0 Move all terms containing b to the left, all other terms to the right. Add '7x' to each side of the equation. 2b + -7x + 7x = 0 + 7x Combine like terms: -7x + 7x = 0 2b + 0 = 0 + 7x 2b = 0 + 7x Remove the zero: 2b = 7x Divide each side by '2'. b = 3.5x Simplifying b = 3.5xSolution
b = {0.5454545455x, 3.5x}
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