# How do you evaluate 7x ^ { 2} - 5x + 6- ( 12x ^ { 2} + 9x - 8)?

Feb 11, 2018

See below.

#### Explanation:

When we see a minus sign by itself without a number in front of the bracket, we need to multiply each term in the bracket by $- 1$.

$\therefore$

$- 1 \cdot 12 {x}^{2} = - 12 {x}^{2}$
$- 1 \cdot 9 x = - 9 x$
$- 1 \cdot - 8 = 8$

This means our expression is now

$7 {x}^{2} - 5 x + 6 - 12 {x}^{2} - 9 x + 8$
Now we simplify by combining like terms (${x}^{2} , x$ and constants).

$\therefore$

Final answer : $- 5 {x}^{2} - 14 x + 14$

Feb 11, 2018

see a step process below;

#### Explanation:

$7 {x}^{2} - 5 x + 6 - \left(12 {x}^{2} + 9 x - 8\right)$

Open the bracket and simplify..

$7 {x}^{2} - 5 x + 6 - 12 {x}^{2} - 9 x + 8$

$7 {x}^{2} - 12 {x}^{2} - 5 x - 9 x + 6 + 8$

$- 5 {x}^{2} - 14 x + 12 \to \text{Quadratic Equation}$

Using;

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

Where;

$a = - 5$

$b = - 14$

$c = 12$

Substituting the values..

x = (-(-14) +- sqrt ((-14)^2 - 4(-5)(12)))/(2(-5)

$x = \frac{14 \pm \sqrt{196 + 240}}{- 10}$

$x = \frac{14 \pm \sqrt{436}}{- 10}$

Hope this helps!

Feb 11, 2018

see a step process below;

#### Explanation:

$7 {x}^{2} - 5 x + 6 - \left(12 {x}^{2} + 9 x - 8\right)$

Open the bracket and simplify..

$7 {x}^{2} - 5 x + 6 - 12 {x}^{2} - 9 x + 8$

$7 {x}^{2} - 12 {x}^{2} - 5 x - 9 x + 6 + 8$

$- 5 {x}^{2} - 14 x + 12 \to \text{Quadratic Equation}$

Using;

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

Where;

$a = - 5$

$b = - 14$

$c = 12$

Substituting the values..

x = (-(-14) +- sqrt ((-14)^2 - 4(-5)(12)))/(2(-5)

$x = \frac{14 \pm \sqrt{196 + 240}}{- 10}$

$x = \frac{14 \pm \sqrt{436}}{- 10}$

Hope this helps!