13b^2-12b-26=1+9b^2

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Solution for 13b^2-12b-26=1+9b^2 equation:


Simplifying
13b2 + -12b + -26 = 1 + 9b2

Reorder the terms:
-26 + -12b + 13b2 = 1 + 9b2

Solving
-26 + -12b + 13b2 = 1 + 9b2

Solving for variable 'b'.

Reorder the terms:
-26 + -1 + -12b + 13b2 + -9b2 = 1 + 9b2 + -1 + -9b2

Combine like terms: -26 + -1 = -27
-27 + -12b + 13b2 + -9b2 = 1 + 9b2 + -1 + -9b2

Combine like terms: 13b2 + -9b2 = 4b2
-27 + -12b + 4b2 = 1 + 9b2 + -1 + -9b2

Reorder the terms:
-27 + -12b + 4b2 = 1 + -1 + 9b2 + -9b2

Combine like terms: 1 + -1 = 0
-27 + -12b + 4b2 = 0 + 9b2 + -9b2
-27 + -12b + 4b2 = 9b2 + -9b2

Combine like terms: 9b2 + -9b2 = 0
-27 + -12b + 4b2 = 0

Factor a trinomial.
(-3 + -2b)(9 + -2b) = 0

Subproblem 1

Set the factor '(-3 + -2b)' equal to zero and attempt to solve: Simplifying -3 + -2b = 0 Solving -3 + -2b = 0 Move all terms containing b to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -2b = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2b = 0 + 3 -2b = 0 + 3 Combine like terms: 0 + 3 = 3 -2b = 3 Divide each side by '-2'. b = -1.5 Simplifying b = -1.5

Subproblem 2

Set the factor '(9 + -2b)' equal to zero and attempt to solve: Simplifying 9 + -2b = 0 Solving 9 + -2b = 0 Move all terms containing b to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -2b = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -2b = 0 + -9 -2b = 0 + -9 Combine like terms: 0 + -9 = -9 -2b = -9 Divide each side by '-2'. b = 4.5 Simplifying b = 4.5

Solution

b = {-1.5, 4.5}

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