The solution of a quadratic equation ax^2 + bx + c = 0 is given by `(-b+-sqrt(b^2 - 4ac))/(2a)` .

For the equation x^2 - 8x + 10 = 0, a = 1, b = -8 and c = 10.

The roots of the equation are : `(8 +- sqrt((-8)^2 - 4*1*10))/(2*1)`

= `(8 +- sqrt(64 - 40))/2`

= `(8 +- sqrt 24)/2`

= `4 +- sqrt 6`

**The roots of the equation x^2 - 8x + 10 = 0 are **`4 +- sqrt 6`

x2 - 8x + 10 = 0

Since it is a quadratic equation, we will apply the formula;

`x={-b+-sqrt(b^2-4ac)}/(2a)`

where,

a = 1

b = - 8

c = 10

Now insert these in the equation;

`x={-(-8)+-sqrt((-8)^2-4(1)(10))}/(2*1)`

`x={8+-sqrt(64-40)}/2`

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`x={8+-sqrt(24)}/2`

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`x={8+-sqrt(2*2*2*3)}/2`

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`x = (8+-2 sqrt(6))/2`

Take 2 common in numerator;

`x=(2(4+-sqrt6))/2`

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Now cancel the 2 of numerator with the 2 in denominator;

`x=4+-sqrt(6)`

Now separating the solutions;

`x=4+sqrt(6),x=4-sqrt(6)`

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Solution Set: {4+sqrt(6),4-sqrt(6)}

Hence Solved!

x^2 - 8x + 10 = 0

Since the above is a quadratic equation we can solve it with the help of a quadratic formula:

x=`{-b+-sqrt(b^2-4ac)} / (2a) `

`Where`

`a=1`

`b=-8`

`c= 10`

`x= {-(-8)+-sqrt(-8^2-4*1*10)} / (2*1)`

`x = {8+-sqrt(64-40)} /2`

`x = {8+-sqrt(24)} /2`

`x = {8+-4sqrt(6)} / 2`

Solution Set= `{ [8+4sqrt(6)]/2, [8-4sqrt(6)]/2 } `

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The easiest way to find solutions for a quadratic equation, in my opinion, is to use the quadratic formula. If this equation factored easily, that would also be a good option, but it does not.

The quadratic formula is `(-b+-sqrt(b^2-4ac))/(2a)`.

With the equation x^2-8x+10, a=1, b=-8, and c=10. Now you can just plug in numbers!

`(-(-8)+-sqrt(-8^2-4(1)(10)))/(2(1))`

`(8+-sqrt(24))/(2)`. The `sqrt(24)` simplifies to be `4sqrt(6) `

Your solutions will be `(8+-4sqrt(6))/(2)` or `4+-4sqrt(6)`