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

Mar 29, 2018

$x = \pm 7$

#### Explanation:

Given   $10 {x}^{2} + 9 = 499$    Solve for $x$

1) Subtract $9$ from both sides to isolate the $10 {x}^{2}$ term

$10 {x}^{2} = 490$

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

${x}^{2} = 49$

3) Find the square roots of both sides

$x = \pm 7$ $\leftarrow$ 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 $7$
$10 \left(49\right) + 9 = 499$ ?

Clear the parentheses
$490 + 9 = 499$ ?

Combine like terms
$499 = 499$

$C h e c k$

Mar 29, 2018

x1 = 7.53
x2 = - 6.63

#### Explanation:

y = 10x^2 + 9x = 499
Use the improved quadratic formula (Socratic search):
$D = {d}^{2} = {b}^{2} - 4 a c = 81 + 19 , 960 = 20 , 041$.
$d = \pm 141.57$
There are 2 real roots:
$x = - \frac{b}{2 a} \pm \frac{d}{2 a} = - \frac{9}{20} \pm \frac{141.57}{20}$
$x = \frac{9 \pm 141.57}{20}$
$x 1 = \frac{150.57}{20} = 7.53$
$x 2 = - \frac{132.57}{20} = - 6.63$
graph{10x^2 +9x - 499 [-320, 320, -160, 160]}