Solve quadratic equation using the square root property.

Question

(2x-9)²-6=43

Answer 1

The first thing we need to do in this equation is get the (2x-9)² by itself, so we need to add 6 to both sides.

(2x - 9)² = 49

Now we need to square root both sides.

√(2x-9)² = √49

When you take the square root of something squared, you're just left with what was being squared.

2x - 9 = ±7 --> Also, remember when you take the square root of a number, you technically have the positive and negative of that number.

It's easier to work with if we write it separately.

2x - 9 = 7 and 2x - 9 = -7

Now let's solve for x for each of them.

2x = 16 --> add 9 to both sides

x = 8 --> divide both sides by 2

Now let's solve the 2nd one.

2x - 9 = -7 --> add 9 to both sides

2x = 2 --> divide both sides by 2

x = 1