Question

How do you solve `x^2+10x=15`?

Answer 1

`x = -5 +- sqrt30`

Here's how I did it:

Explanation:

`x^2 + 10x = 15`

First, we want to set one side to `0` and let one side have `3` terms so that we can factor it, so we subtract `15` from both sides of the equation:
`x^2 + 10x - 15 = 0`

Now we factor. We have to find two numbers that:

• Multiply up to `-15`
• Add up to `10`.

We know that the factors of `-15` are `-15, -5, -3, -1, 1, 3, 5,` and `15`. However, no group of factors of `-15` can add up to `10`, so we have to do another method, called the quadratic formula.

The quadratic formula is `x = (-b +- sqrt(b^2 - 4ac))/(2a)`.

Our equation is in the form of `ax^2 + bx^2 + c`, which is also called standard form. So we know that:
`a = 1`

`b = 10`

`c = -15`

Now let's substitute these values into the quadratic formula:
`x = (-10 +- sqrt(10^2 - 4(1)(-5)))/(2(1))`

Simplify by doing `10^2`, `-4(1)(-5)`, and `2(1)`:
`x = (-10 +- sqrt(100 + 20))/2`

Add `100 + 20`:
`x = (-10 +- sqrt(120))/2`

Radicalize/simplify `120`
`x = (-10 +- sqrt(4*30))/2`

`x = (-10 +- 2sqrt30)/2`

Divide by `2`:
`x = -5 +- sqrt30`

Hope this helps!