Question

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

Answer 1

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√(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 * 9) }}{2 * 5}`

`\rm \implies \: x = \cfrac{-1 8 \pm √(324- 20 * 9) )}{10}`

`\rm \implies \: x = \cfrac{-1 8 \pm √(324- 180)}{10}`

`\rm \implies \: x = \cfrac{ - 18 \pm √(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.

Answer 2

`x = -3~\text{and}~ x = -\frac 35`

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 = -\frac 35`