Solve x^2 + 2x = 15 Step by Step | Quadratic equations

Step by step

The question

Question: solve x² + 2x = 15.

x² + 2x = 15

1 Get 0 on one side

To solve it, we want 0 on the right side.

So we take away 15 on both sides.

We do it on both sides, so they stay equal.

x² + 2x − 15 = 15 − 15

Now we have x² + 2x − 15 = 0.

x² + 2x − 15 = 0

2 Factor

We need two numbers.

They multiply to −15, and they add to 2.

? × ? = −15

? + ? = 2

They multiply to a minus number, so one number is plus and one is minus.

They add to a plus number, so the bigger one is plus.

× is − → one +, one −; bigger one +

We list the pairs that make 15, smallest first.

We take the smaller from the bigger.

We need 2.

3 and 5 give 2.

Yes!

With the signs: −3 and 5.

1 × 15: 15 − 1 = 14

3 × 5: 5 − 3 = 2 ✓

So it is (x − 3)(x + 5) = 0.

(x − 3)(x + 5) = 0

3 One bracket is 0

Two numbers multiply to 0.

That only happens if one of them is 0.

So one bracket must be 0.

A × B = 0 → A = 0 or B = 0

We make each bracket 0.

Two small equations.

x − 3 = 0 or x + 5 = 0

In x − 3 = 0, we add 3 on both sides.

In x + 5 = 0, we take away 5 on both sides.

x − 3 + 3 = 0 + 3 or x + 5 − 5 = 0 − 5

So x = 3 or x = −5.

x = 3 or x = −5

4 Check

Let's check: put x = 3 into the left side.

x = 3: 3² + 2(3) = 9 + 6 = 15

We get 15, the same as the right side.

It works!

Now put x = −5 into the left side.

x = −5: (−5)² + 2(−5) = 25 − 10 = 15

We get 15 again, the same as the right side.

So both answers are right!

Let's look back.

First: get 0 on one side.

Then: factor.

Then: one bracket is 0.

Last: check.

Answer