Question

solve using formula x²+7x+12=0​

Answer 1

GIVEN :-

• A quadratic equation x² + 7x + 12 = 0.

TO FIND :-

• The value of x.

SOLUTION :-

$\\ : \implies \displaystyle \sf \: x ^{2} + 7x + 12 = 0$

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

• a = 1.
• b = 7.
• c = 12.

$\\ \\ : \implies \displaystyle \sf \:x = \frac{ - 7 \pm \sqrt{(7) ^{2} - 4 \times 1 \times 12} }{2 \times 1}$

$: \implies \displaystyle \sf \:x = \frac{ - 7 \pm \sqrt{49 - 48} }{2}$

$: \implies \displaystyle \sf \:x = \frac{ - 7 \pm \sqrt{1} }{2}$

$: \implies \displaystyle \sf \:x = \frac{ - 7 - 1}{2} \: , \: x = \frac{ - 7 + 1}{2}$

$: \implies \displaystyle \sf \:x = \frac{ - 8}{2} \: , \: x = \frac{ - 6}{2}$

$: \implies \underline{ \boxed{ \displaystyle \pink{ \mathfrak{\:x = - 4 \: , \: x = - 3}}}}$

Answer 2

$\underline{\underline{\sf{\maltese\:\:Question}}}$

$\bf{\bigstar\:\:\:\:Solve\:\:for\:\:x\:\::x^2+7x+12=0}$

$\underline{\underline{\sf{\maltese\:\:Answer}}}$

$\bf{\bullet\:\:\:x=-3,\:x=-4}$

$\underline{\underline{\sf{\maltese\:\:Calculations}}}$

$\bf{x^2+7x+12=0}$

Solve with the Quadratic Formula

$\sf{Quadratic\:Equation\:Formula:}$

$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}$

$\sf{x_{1,\:2}=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}$

$\mathrm{For\:}\quad a=1,\:b=7,\:c=12$

$\sf{x_{1,\:2}=\dfrac{-7\pm \sqrt{7^2-4\cdot \:1\cdot \:12}}{2\cdot \:1}}$

$\implies\sf{x_{1,\:2}=\dfrac{-7\pm \sqrt{49-48}}{2\cdot \:1}}$

$\implies\sf{x_{1,\:2}=\dfrac{-7\pm \sqrt{1}}{2\cdot \:1}}$

$\implies\sf{x_{1,\:2}=\dfrac{-7\pm 1}{2\cdot \:1}}$

$\mathrm{Separate\:the\:solutions}$

$\implies\sf{\displaystyle x_1=\frac{-7+1}{2\cdot \:1},\:x_2=\frac{-7-1}{2\cdot \:1}}$

$\implies\sf{\displaystyle x_1=\frac{-6}{2},\: x_2=\frac{-8}{2}}$

$\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}$

$\boxed{\bf{x=-3,\:x=-4}}$