Solve using the Quadratic Formula. Solve. Find all complex number solutions

Question

x²=3x+5

Answer 1

Ruby, I just saw Bryon's answer.  His approach is right on !   Let me approach it from a different perspective... maybe I can help you !   First, try the problem from the  FOIL  perspective.  Most students will approach these problems this way, because it's faster.   However, you'll quickly see that  only  5  and 1   can be used, and there's no way you can get the  -3  in the middle.  That's the reason you turn to the quadratic formula....that always works!   A complex solution occurs when the determinant ( that's the value of the answer under the radical sign, when all of that is simplified) results in a negative value.  This doesn't happen too often, but when it does, we have complex numbers in the solution.

X squared  -3X - 5  =  0   has  a=1   b=  -3   and  c = -5   You will plug these values into the formula that Bryon did for you in the middle of his solution.  That reads   "  negative b  plus or minus  the square root of  b squared   minus  4AC  all divided by  2A ".     so,  X  =   3  +-  sqrt(  9  -   4( 1 )( -5)  )  all divided by  2(1).  Go ahead, and write that down.

The inside of the square root becomes   9  +  20  after you simplify signs.   That's where you get his  29.   OK??

Now, since  29  is positive, then the answer has  2  possible solutions. ( square roots cannot be negative ).  Therefore, the answer has no complex parts.   The "plus or minus" part tells you there are usually two solutions.  You either add the parts "upstairs" or you subtract them.  I hope this helps you, now.  Take care and contact us, again.

 

Charles S.

Hendersonville, NC.

Answer 2

Whenever you're solving a quadratic equation, the first thing you need to do is get all the terms on one side, so the sum (or difference) of them equals 0. Here, subtract 3x and 5 from both sides to get

1x²-3x-5=0

 

The quadratic formula uses the values of a, b, and c, the coefficients of the three terms. I've color coded them to be more obvious, and included the (usually) unwritten 1.

 

The quadratic formula is x = (-b ± √[b²-4ac])/(2a)

 

Plug the values in and simplify to find your solutions. Since this question refers to complex solutions, lets look at the part under the square root, callled the determinant. [b²-4ac] = [(-3)²-4(1)(-5)] = 9+20 = 29. Since the discriminant is positive, the square root of it is a real (but irrational) number. There are no complex solutions, and you just need to plug in the values!