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

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

Step-by-step 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:

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

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step-by-step explanation: