Question

solve
${x }^{2} - 2x - 44 = 0$
​

Answer 1

Solve Quadratic Equation using the Quadratic Formula

2.3 Solving x2+2x-44 = 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 = 2

C = -44

Accordingly, B2 - 4AC =

4 - (-176) =

180

Applying the quadratic formula :

-2 ± √ 180

x = ——————

2

Can √ 180 be simplified ?

Yes! The prime factorization of 180 is

2•2•3•3•5

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).

√ 180 = √ 2•2•3•3•5 =2•3•√ 5 =

± 6 • √ 5

√ 5 , rounded to 4 decimal digits, is 2.2361

So now we are looking at:

x = ( -2 ± 6 • 2.236 ) / 2

Two real solutions:

x =(-2+√180)/2=-1+3√ 5 = 5.708

or:

x =(-2-√180)/2=-1-3√ 5 = -7.708