Question

Consider the following equation. 0 = x2 - 10x - 27

Answer 1

x = -27/8

Explanation:

First lets rearrange --> Changed x2 to 2x:

0 = 2x - 10x - 27

Next lets simplify more:

0 = -8x - 27

Now lets add 8x to the 0 and 27 to that:

0 + 8x + 27 = 0

So we have:

8x + 27 = 0

Lets minus the 27 from the 0:

8x = 0 - 27

Now lets divide both sides by 8 to get:

x = -27/8

Answer 2

x = 5 + 2 sqrt(13) or x = 5 - 2 sqrt(13)

Explanation:

Solve for x over the real numbers:

0 = x^2 - 10 x - 27

0 = x^2 - 10 x - 27 is equivalent to x^2 - 10 x - 27 = 0:

x^2 - 10 x - 27 = 0

Add 27 to both sides:

x^2 - 10 x = 27

Add 25 to both sides:

x^2 - 10 x + 25 = 52

Write the left hand side as a square:

(x - 5)^2 = 52

Take the square root of both sides:

x - 5 = 2 sqrt(13) or x - 5 = -2 sqrt(13)

Add 5 to both sides:

x = 5 + 2 sqrt(13) or x - 5 = -2 sqrt(13)

Add 5 to both sides:

Answer: x = 5 + 2 sqrt(13) or x = 5 - 2 sqrt(13)