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

Sagot :

loneguy

Answer:

[tex]x = -3~\text{and}~ x = -\dfrac 35[/tex]

Step-by-step explanation:

[tex]~~~~~~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[/tex]

Itz5151

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

[tex] \rm x=\cfrac{-b\pm\sqrt{b^2-4ac}}{2}[/tex]

According to the question,on the formula,

  • a = 5
  • b = 18
  • c = 9

So substitute them on the formula:

THEN solve for x.

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

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

[tex]\rm \implies \: x = \cfrac{-1 8 \pm \sqrt{324- 180}}{10} [/tex]

[tex] \rm \implies \: x = \cfrac{ - 18 \pm \sqrt{144} }{10} [/tex]

[tex] \rm \implies \: x = \cfrac{ - 18 \pm12}{10}[/tex]

[tex] \rm \implies \: x = \cfrac{9 \pm 6}{5} [/tex]

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

[tex] \rm \implies \boxed{x = - \cfrac{3 }{5} }[/tex]

[tex] \implies \boxed{\rm x = - 3}[/tex]

So there'll be two possible answers.

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