Question 80885
Solve for b?
{{{b^4+13b^2+36 = 0}}} Let's temporarily swap variables: {{{b^2 = x}}} so then {{{b^4 = x^2}}} Now rewrite the equation:
{{{x^2+13x+36 = 0}}} Solve for x by factoring.
{{{(x+4)(x+9) = 0}}} Apply the zero products principle:
{{{x+4 = 0}}} and/or {{{x+9 = 0}}}
If {{{x+4 = 0}}} then {{{x = -4}}}
If {{{x+9 = 0}}} then {{{x = -9}}}
Now replace the x with {{{b^2}}}
For {{{x = -4}}} we get:
{{{b^2 = -4}}} Take the square root of both sides.
{{{b = sqrt(-4)}}} or {{{b = -sqrt(-4)}}}
{{{b = 2sqrt(-1)}}} or {{{b = -2sqrt(-1)}}}
{{{b = 2i}}} or {{{b = -2i}}}
For {{{x = -9}}} we get:
{{{b^2 = -9}}} Take the square root of both sides.
{{{b = sqrt(-9)}}} or {{{b = -sqrt(-9)}}}
{{{b = 3sqrt(-1)}}} or {{{b = -3sqrt(-1)}}}
{{{b = 3i}}} or {{{b = -3i}}}
So the four solutions are: {{{i = sqrt(-1)}}}
{{{b = 2i}}}
{{{b = -2i}}}
{{{b = 3i}}}
{{{b = -3i}}}