Question

7x^2-26x-8 splitting the middle term​

Answer 1

7x^2 - 26x - 8 = 0

7x^2 - 28x + 2x - 8 = 0

7x ( x - 4 ) + 2 ( x - 4 ) = 0

(x - 4) (7x + 2) = 0

x - 4 = 0. 7x + 2 = 0

x = 4. x = -2/7

The roots are 4 and -2/7.

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Value\:of\:x=4\:and\:\frac{-2}{7}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green {\underline \bold{given : }} \\ \tt{: \implies 7 {x}^{2} - 26x - 8 = 0} \\ \\ \red{\underline \bold{to \: find : }} \\ \tt{: \implies x = ?}$

• According to given question :

$\bold{solving \: by \: middle \: term \: spiliting} \\ \tt{: \implies {7x}^{2} - 26x - 8 = 0 }\\ \\ \tt{: \implies {7x}^{2} - 28x + 2x - 8 = 0} \\ \\ \tt{: \implies 7x(x - 4) + 2(x - 4) = 0} \\ \\ \tt{: \implies (7x + 2)(x - 4) = 0} \\ \\ \green{\tt{: \implies x = \frac{ - 2}{7} \: and \: 4}}$

$\text{Alternate \: method} \\ \\ \bold{By \: Qudratic \: fomula} \\ \tt{: \implies {7x}^{2} - 26x - 8 = 0} \\ \\ \tt{: \implies x = \frac{ - ( - 26) \pm \sqrt{ {( - 26)}^{2} - 4 \times 7 \times ( - 8) } }{2 \times 7} } \\ \\ \tt{: \implies x = \frac{26 \pm \sqrt{676 + 224} }{14}} \\ \\ \tt{: \implies x = \frac{26 \pm \sqrt{900} }{14} } \\ \\ \tt{: \implies x = \frac{26 \pm30}{14}} \\ \\ \green{\tt{: \implies x = \frac{ - 2}{7} \: and \: 4}}$