Question

answer this problem ײ +9x + 14 =0​

Answer 1

$\textsf{\large{\underline{Solution}:}}$

Given Equation:

$\rm: \longmapsto {x}^{2} + 9x + 14 = 0$

By splitting the middle term, we get:

$\rm: \longmapsto {x}^{2} + (7 + 2)x + 14 = 0$

$\rm: \longmapsto {x}^{2} +7x + 2x + 14 = 0$

$\rm: \longmapsto x(x +7) + 2(x + 7) = 0$

$\rm: \longmapsto (x+ 2)(x + 7) = 0$

By zero product rule, we get:

$\rm: \longmapsto \begin{cases} \rm (x+ 2) = 0 \\ \rm(x + 7) =0 \end{cases}$

Therefore:

$\rm: \longmapsto x = - 2, - 7$

★ So, the values of x satisfying the given equation are -2 and -7.

$\textsf{\large{\underline{Verification}:}}$

Put x = -2 in LHS, we get:

$\rm = {( - 2)}^{2} + 9 \times ( - 2) + 14$

$\rm = 4 - 18 + 14$

$\rm = 0$

Put x = -7 in LHS, we get:

$\rm = {( - 7)}^{2} + 9 \times ( - 7) + 14$

$\rm = 49 - 63+ 14$

$\rm = 0$

Hence, our answers are correct (Verified).

$\textsf{\large{\underline{Final Answer}:}}$

• The values of x satisfying the given equation are -2 and -7.

Answer 2

Equation given to us:

• x² + 9x + 14

Using Formula,

Quadratic formula:-

• $\purple{ \underline{{\boxed{ \bf{x \: = \: \dfrac{ - b± \sqrt{b {}^{2} - 4ac } }{2a} }}}}}$

Here we have:

• a is 1
• b is 9
• c is 14

Substituting the values:

$\longrightarrow \: \sf{x \: = \: \dfrac{ - 9± \sqrt{(9) {}^{2} - 4(1)(14) } }{2(1)} }$

$\longrightarrow \: \sf{x \: = \: \dfrac{ - 9± \sqrt{(9) {}^{2} - 4 \times 1 \times 14} }{2(1)} }$

$\longrightarrow \: \sf{x \: = \: \dfrac{ - 9± \sqrt{(9) {}^{2} - 4 \times 1 \times 14} }{2 \times 1} }$

$\longrightarrow \: \sf{x \: = \: \dfrac{ - 9± \sqrt{(9) {}^{2} - 4\times 14} }{2 } }$

$\longrightarrow \: \sf{x \: = \: \dfrac{ - 9± \sqrt{(9) {}^{2} - 56} }{2 } }$

$\longrightarrow \: \sf{x \: = \: \dfrac{ - 9± \sqrt{(9 \times 9)- 56} }{2 } }$

$\longrightarrow \: \sf{x \: = \: \dfrac{ - 9± \sqrt{(81)- 56} }{2 } }$

$\longrightarrow \: \sf{x \: = \: \dfrac{ - 9± \sqrt{81- 56} }{2 } }$

$\longrightarrow \: \sf{x \: = \: \dfrac{ - 9± \sqrt{25} }{2 } }$

$\longrightarrow \: \sf{x \: = \: \dfrac{ - 9 \: ± \:5 }{2 } }$

Now,

$: \leadsto\: \sf{x \: = \: \dfrac{ - 9 \: - \:5 }{2 } }$

$: \leadsto\: \sf{x \: = \: \dfrac{ - 14 }{2 } }$

$: \leadsto\: \sf{x \: = \: \cancel\dfrac{ - 14 }{2 } }$

$: \leadsto\: \large\pink{ \underline{ \boxed{ \bf{x \: = \: - 7 }}}}$

Also,

$: \leadsto\: \sf{x \: = \: \dfrac{ - 9 \: + \:5 }{2 } }$

$: \leadsto\: \sf{x \: = \: \dfrac{ - 4 }{2 } }$

$: \leadsto\: \sf{x \: = \: \cancel\dfrac{ - 4 }{2 } }$

$: \leadsto \: \large\pink{ \underline{ \boxed{ \bf{x \: = \: - 2 }}}}$

• $\underline{ \bf{Hence, \: the \: two \: values \: of \: x \: are \: - 2 \: and \: - 7}}$

Additional Information:

• An equation which has only one variable in which highest power of variable is two, is known as quadratic equation.
• The standard form of a quadratic equation is ax²+bx+c = 0, where a, b and c are all real numbers.

Discriminant formula:-

• D = b² - 4ac

Here,

• D is discriminant