Question

Solve the following quadratic equation 5x^2+18x+9=0

Answer 1

Answer:

$x = -3~\text{and}~ x = -\dfrac 35$

Step-by-step explanation:

$~~~~~~5x^2 +18x +9=0\\\\\implies 5x^2 +15x +3x +9 = 0\\\\\implies 5x(x+3) +3(x+3) = 0\\\\\implies (x+3)(5x+3) = 0\\\\\implies x = -3,~ x = -\dfrac 35$

Answer 2

Answer:

x = -3

OR

x = -(3/5)

Step by step explanation:

Given:

• 5x^2+18x+9=0

To Find:

• x

Soln:

Use quadratic formulae:

• Here I typed Quadratic formula as x

$\rm x=\cfrac{-b\pm\sqrt{b^2-4ac}}{2}$

According to the question,on the formula,

• a = 5
• b = 18
• c = 9

So substitute them on the formula:

THEN solve for x.

$\rm \implies \: x = \cfrac{-1 8 \pm \sqrt{18 {}^{2} - 4(5 \times 9) }}{2 \times 5}$

$\rm \implies \: x = \cfrac{-1 8 \pm \sqrt{324- 20 \times 9) }}{10}$

$\rm \implies \: x = \cfrac{-1 8 \pm \sqrt{324- 180}}{10}$

$\rm \implies \: x = \cfrac{ - 18 \pm \sqrt{144} }{10}$

$\rm \implies \: x = \cfrac{ - 18 \pm12}{10}$

$\rm \implies \: x = \cfrac{9 \pm 6}{5}$

Final solution will after adding first(9+6),then secondly subtracting both 9-6

$\rm \implies \boxed{x = - \cfrac{3 }{5} }$

$\implies \boxed{\rm x = - 3}$

So there'll be two possible answers.