Question

How do you solve `10x^2+9=499`?

Answer 1

`x = +- 7`

Explanation:

Given   `10x^2+9=499`    Solve for `x`

1) Subtract `9` from both sides to isolate the `10x^2` term

`10x^2=490`

2) Divide both sides by `10` to make the numbers smaller

`x^2 = 49`

3) Find the square roots of both sides

`x = +- 7` `larr` answer

---------- Check ----------

Sub in `7` (or `-7`) in the place of `x` in the original equation

`10   x^2 +9=499`
`10 (7^2)+9=499` ?

Clear the exponent by squaring the `7`
`10(49) + 9 = 499` ?

Clear the parentheses
`490 + 9 = 499` ?

Combine like terms
`499 = 499`

`Check`

Answer 2

x1 = 7.53
x2 = - 6.63

Explanation:

y = 10x^2 + 9x = 499
Use the improved quadratic formula (Socratic search):
`D = d^2 = b^2 - 4ac = 81 + 19,960 = 20,041`.
`d = +- 141.57`
There are 2 real roots:
`x = -b/(2a) +- d/(2a) = - 9/20 +- 141.57/20`
`x = (9 +- 141.57)/20`
`x1 = 150.57/20 = 7.53`
`x2 = - 132.57/20 = - 6.63`
graph{10x^2 +9x - 499 [-320, 320, -160, 160]}