Question

5x²-12x-9=0 by all methods

Answer 1

Step-by-step explanation:

Solve by factors.

\displaystyle 5x^2-12x-95x2−12x−9

(5x^2+3x)+(-15x-9)(5x2+3x)+(−15x−9)

Solve.

5x^2+3x=x(5x+3)5x2+3x=x(5x+3)

\displaystyle -3*5x-3*3−3∗5x−3∗3

Common term of 3.

\displaystyle -3(5x+3)−3(5x+3)

\displaystyle x(5x+3)-3(5x+3)x(5x+3)−3(5x+3)

Common term of 5x+3.

\displaystyle(5x+3)(x-3)(5x+3)(x−3)

\displaystyle (5x+3)(x-3)=0(5x+3)(x−3)=0

\displaystyle 5x+3=05x+3=0

Subtract by 3 from both sides.

\displaystyle 5x+3-3=0-35x+3−3=0−3

Solve.

\displaystyle 5x=-35x=−3

Divide by 5 from both sides.

\displaystyle \frac{5x}{5}=\frac{-3}{5}55x=5−3

Solve.

\Large\boxed{x=-\frac{3}{5}}x=−53

\displaystyle x-3=0x−3=0

Then, you add by 3 from both sides.

\displaystyle x-3+3=0+3x−3+3=0+3

Solve.

Add the numbers from left to right.

\displaystyle 0+3=\boxed{3}0+3=3

\Large\boxed{X=3}X=3

\Large\boxed{X=-\frac{3}{5}, \quad X=3}

x=3 or x=-3/5

Answer 2

Step-by-step explanation:

$5 {x}^{2} - 12x - 9 = 0$

By using quardratic formula,

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

$x = \frac{ - ( - 12) \pm \sqrt{ {12}^{2} - 4(5)( - 9)} }{2(5)}$

=> $x = \frac{12\pm \sqrt{144 + 180} }{10}$

=> $x = \frac{12\pm \sqrt{324} }{10}$

=> $x = \frac{12\pm18}{10}$

=> $\boxed{x = \frac{12 + 18}{10} = \frac{30}{10} = 3 }$

=> $\boxed{x = \frac{12 - 8}{10} = \frac{ - 6}{10} = - \frac{ 3}{5} }$

By completing the square,

$5 {x}^{2} - 12x - 9 = 0$

=> $5 {x}^{2} - 12x = 9$

multiplying $\frac{1}{5}$ to both sides

=> $\frac{1}{5} (5 {x}^{2} - 12x ) = \frac{1}{5} (9)$

=> ${x}^{2} - \frac{12}{5} x = \frac{9}{5}$

adding $( \frac{12}{10} )^{2}$ to both sides,

=> ${x}^{2} - \frac{12}{5} x + { (\frac{12}{10}) }^{2} = \frac{9}{5} + {( \frac{12}{10} )}^{2}$

=> ${(x - \frac{12}{10} )}^{2} = \frac{9}{5} + \frac{144}{100}$

=> ${(x - \frac{12}{10} )}^{2} = \frac{324}{100}$

=> $x - \frac{12}{10} =\pm \sqrt{ \frac{324}{100} }$

=> $x = \pm \frac{18}{10} + \frac{12}{10}$

=> $\boxed{x = \frac{18}{10} + \frac{12}{10} = \frac{30}{10} = 3}$

=> $\boxed{x = - \frac{18}{10} + \frac{12}{10} = \frac{ - 6}{10} = - \frac{ 3}{5}}$

By Factorization,

$5 {x}^{2} - 12x - 9 = 0$

=> $5 {x}^{2} - 15x + 3x - 9 = 0$

=> $5x(x - 3) + 3(x - 3) = 0$

=> $(x - 3)(5x + 3) = 0$

=> $x - 3 = 0$ => $x = 3$

=> $5x + 3 = 0$ => $x = - \frac{3}{5}$