SOLUTION: 17. Express the roots of 9x^2 + 40 = 36x in simplest (a + bi) form. Thanks happy new years

Question 174716This question is from textbook Amsco's Preparing for the Regents Examination Mathematics B
: 17.
Express the roots of 9x^2 + 40 = 36x in simplest (a + bi) form.
Thanks happy new years This question is from textbook Amsco's Preparing for the Regents Examination Mathematics B

Found 2 solutions by Mathtut, jim_thompson5910:
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!

roots

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

The discriminant -144 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

In the field of imaginary numbers, the square root of -144 is + or - .

The solution is , or
Here's your graph:

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given equation.

Subtract 36x from both sides.

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Break up the fraction for each case.

or Reduce.

So the answers are or

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