Question

solve the quadratic equation 9x'2+7x-2​

Answer 1

Answer:

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Answer 2

Given :

• 9x² +7x - 2

To Find :

• Value of x

Solution :

Method 1 :-

By splitting middle term

$\sf \implies 9 {x}^{2} +9x - 2x - 2 = 0 \\ \\ \sf \implies9x(x + 1) - 2(x + 1) = 0\\ \\ \sf \implies(9x - 2)(x + 1) = 0 \\ \\ \sf \implies9x - 2 = 0 \\ \\ \implies \boxed{ \sf x = \frac{2}{9}} \\ \\ \sf \implies x + 1 = 0 \\ \\ \implies \boxed{ \sf x = - 1}$

Method 2 :-

By using quadratic formula

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

Here

• a = 9
• b = 7
• c = - 2

Substitute values in formula

$\implies \sf x = \frac{ - 7 \pm \sqrt{ {7}^{2} - 4 \times 9( - 2)} }{ 2 \times 9} \\ \\ \implies \sf x = \frac{ - 7 \pm \sqrt{49 + 72} }{18} \\ \\ \implies \sf x = \frac{ - 7 \pm \sqrt{121} }{18} \\ \\ \implies \sf x = \frac{ - 7 \pm 11 }{18}$

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$\implies \sf x = \frac{ - 7 + 11}{18} \\ \\ \implies \sf x = \frac{4}{18} \\ \\ \implies \boxed{ \sf x = \frac{2}{9}}$

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$\implies \sf x = \frac{ - 7 - 11}{18} \\ \\ \implies \sf x = \frac{ - 18}{18} \\ \\\implies \boxed{ \sf x = - 1}$