how to solve for x^2-2x+5=0

Question

solve using the quadratic formula



Answer 1

The general formula for a quadratic equation is:

ax^2+bx+c=0

where a, b, and c are given, real numbers, usually integers. The quadratic formula is used to solve for x such that plugging the values found into the quadratic equation will result in the equation being equal to zero. The quadratic formula is:

 x = (-b ±√(b^2 – 4ac))/2a

Note that the ± symbol shows that there are two possible solutions. They could be real, the same (often referred to as repeated roots), or complex, depending on whether b²-4ac is positive, zero, or negative.

In this problem,

a=1

b=-2

c=5

The quadratic formula is then:

X=(-(-2)±√((-2)²-4(1*5))/2(1)

X=(2±√((4-20))/2

X=1±√(-16)/2

Because b²-4ac < 0, we know we have a complex number solution. Thus:

X=1±√(-16)/2

X=1±((√16)(√(-1)))/2

X=1±(4i)/2, where i refers to √(-1)

X=1±2i

Put another way, x=1+2i and x=1-2i are the two solutions satisfying the equation.

This is the required answer.

You should verify the answer by plugging each of the two values into the original quadratic equation to verify they result in zero.