Solve for the roots in simplest form using the quadratic formula:
x2 – 14x = -50

Solving x2-14x+58 = 0 by the Quadratic Formula .

According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B2-4AC

x = ————————

2A

In our case, A = 1

B = -14

C = 58

Accordingly, B2 - 4AC =

196 - 232 =

-36

Applying the quadratic formula :

14 ± √ -36

x = ——————

2

In the set of real numbers, negative numbers do not have square roots. A new set of numbers, called complex, was invented so that negative numbers would have a square root. These numbers are written (a+b*i)

Both i and -i are the square roots of minus 1

Accordingly,√ -36 =

√ 36 • (-1) =

√ 36 • √ -1 =

± √ 36 • i

Can √ 36 be simplified ?

Yes! The prime factorization of 36 is

2•2•3•3

To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 36 = √ 2•2•3•3 =2•3•√ 1 =

± 6 • √ 1 =

± 6

So now we are looking at:

x = ( 14 ± 6i ) / 2

Two imaginary solutions :

x =(14+√-36)/2=7+3i= 7.0000+3.0000i

or:

x =(14-√-36)/2=7-3i= 7.0000-3.0000i

Two solutions were found :

x =(14-√-36)/2=7-3i= 7.0000-3.0000i

x =(14+√-36)/2=7+3i= 7.0000+3.0000i

Step-by-step explanation:

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"i" is used to represent surd form because it doesn't have a whole number as it's square root.

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step-by-step explanation:

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