Question

What are the solutions to the equation x^2-8x=10?

Answer 1

x = 4 ±
`√(26)` OR x = 4 -
`√(26)`, 4 +
`√(26)`

Explanation:

To solve these equation we create a trinomial and then solve for x.

First we are going to move all terms to one side and make sure we can set the equation equal to zero. To do so, we are going to subtract 10 from both sides.
x² - 8x - 10 = 10 - 10
Simplify:
x² - 8x - 10 = 0

At this point, we think about if there are any factors of -10 with a sum equal to -8. This is one of the easier ways to factor a trinomial and then solve for x. Unfortunately, no factors of -10 with a sum equal to -10. So, because the equation is now in the form ax² + bx + c = 0, where a and b are the numbers in front of our variables and c is a constant we can use the quadratic formula to solve for x.
a = 1
b = -8
c = -10

The quadratic formula:
x = (-b ±
`\sqrt{b^(2)-4ac}`) / 2a

And with this we can plug and play, simplifying along the way:
x = (-(-8) ±
`\sqrt{(-8)^(2)- 4(1)(-10)}`) / 2(1)
x = (8 ±
`√(64 - (-40))`) / 2
x = (8 ±
`√(104)`) / 2
Factor 104 into 4 times 26 because we can take the square root of 4.
x = (8 ±
`√(4(26))`) / 2
x = (8±
`2√(26)`) / 2
Now we can separate and divide each term in the numerator by the 2 in the denominator to simplify.
x = (8 / 2) ± (
`2√(26)` / 2)

x = 4 ±
`√(26)`, this can be your answer or you can separate them because of the plus/minus into two solutions:

x = 4 -
`√(26)`, 4 +
`√(26)`