Question

Solve the equation for x.
x2 = 36
The solutions to the equation are
and

Answer 1

x2=36

We move all terms to the left:

x2-(36)=0

We add all the numbers together, and all the variables

x^2-36=0

a = 1; b = 0; c = -36;

Δ = b2-4ac

Δ = 02-4·1·(-36)

Δ = 144

The delta value is higher than zero, so the equation has two solutions

We use following formulas to calculate our solutions:

x1=−b−Δ√2ax2=−b+Δ√2a

Δ‾‾√=144‾‾‾‾√=12

x1=−b−Δ√2a=−(0)−122∗1=−122=−6

x2=−b+Δ√2a=−(0)+122∗1=122=6

Answer 2

9514 1404 393

Answer:

x = -6 or +6

Explanation:

You know from your multiplication tables that 6×6 = 36, so one answer is ...

x = 6

You also know that the product of two negative numbers is positive, so another answer is ...

x = -6

__

Check

x² = 6² = 6×6 = 36

x² = (-6)² = (-6)×(-6) = 36

_____

Alternate approach

If you like, you can rewrite the equation as ...

x² -36 = 0

This can be factored to ...

(x -6)(x +6) = 0

The zero product rule tells you this product will only be zero if one or the other factors is zero.

x -6 = 0 ⇒ x = 6

x +6 = 0 ⇒ x = -6

The two solutions are x = ±6.