Question

Solve through formula method:
x^2+3x-28=0

Need ASAP!​

Answer 1

$\huge \sf {\orange{\underline{\purple{\underline{Question :-}}}}}$

$\sf{Solve :\:x^2+3x-28=0}$

$\huge \sf {\orange {\underline {\pink{\underline{Answer :-}}}}}$

$\large\boxed{\sf{x=4,\:x=-7}}$

$\underline{\underline{\sf{x^2+3x-28=0}}}$

Solve with the quadratic formula

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

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

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

For

a = 1

b = 3

c = -28

$\sf{x_{1,\:2}=\dfrac{-3\pm \sqrt{3^2-4\cdot \:1\cdot \left(-28\right)}}{2\cdot \:1}}$

$\sf{x_{1,\:2}=\dfrac{-3\pm \sqrt{3^2+4\cdot \:1\cdot \:28}}{2\cdot 1}}$

$\sf{x_{1,\:2}=\dfrac{-3\pm \sqrt{3^2+112}}{2\cdot 1}}$

$\sf{x_{1,\:2}=\dfrac{-3\pm \sqrt{9+112}}{2\cdot 1}}$

$\sf{x_{1,\:2}=\dfrac{-3\pm \sqrt{121}}{2\cdot 1}}$

$\sf{x_{1,\:2}=\dfrac{-3\pm \sqrt{11^2}}{2\cdot 1}}$

$\sf{x_{1,\:2}=\dfrac{-3\pm \:11}{2\cdot \:1}}$

Separate the solutions

$\sf{\displaystyle x_1=\frac{-3+11}{2\cdot \:1},\:x_2=\frac{-3-11}{2\cdot \:1}}$

$--------------------$

$\sf{x=\dfrac{-3+11}{2\cdot \:1}}$

$\sf{x=\dfrac{8}{2\cdot \:1}}$

$\sf{x=\dfrac{8}{2}}$

$\bf{x=4}$

$--------------------$

$\sf{\displaystyle x=\frac{-3-11}{2\cdot \:1}}$

$\sf{x=\dfrac{-14}{2\cdot \:1}}$

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

$\bf{x=-7}$

$--------------------$

The solutions to the quadratic equation are :

$\large\boxed{\sf{x=4,\:x=-7}}$

${\huge{\underline{\small{\mathbb{\pink{HOPE\:HELPS\:UH :)}}}}}}$

$\red{\tt{sωєєтcнαям♡~}}$

Answer 2

$\huge \sf {\orange{\underline{\purple{\underline{Question :-}}}}}$

$\sf{Solve :\:x^2+3x-28=0}$

$\huge \sf {\orange {\underline {\pink{\underline{Answer :-}}}}}$

$\large\boxed{\sf{x=4,\:x=-7}}$

$\underline{\underline{\sf{x^2+3x-28=0}}}$

Solve with the quadratic formula

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

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

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

For

a = 1

b = 3

c = -28

$\sf{x_{1,\:2}=\dfrac{-3\pm \sqrt{3^2-4\cdot \:1\cdot \left(-28\right)}}{2\cdot \:1}}$

$\sf{x_{1,\:2}=\dfrac{-3\pm \sqrt{3^2+4\cdot \:1\cdot \:28}}{2\cdot 1}}$

$\sf{x_{1,\:2}=\dfrac{-3\pm \sqrt{3^2+112}}{2\cdot 1}}$

$\sf{x_{1,\:2}=\dfrac{-3\pm \sqrt{9+112}}{2\cdot 1}}$

$\sf{x_{1,\:2}=\dfrac{-3\pm \sqrt{121}}{2\cdot 1}}$

$\sf{x_{1,\:2}=\dfrac{-3\pm \sqrt{11^2}}{2\cdot 1}}$

$\sf{x_{1,\:2}=\dfrac{-3\pm \:11}{2\cdot \:1}}$

Separate the solutions

$\sf{\displaystyle x_1=\frac{-3+11}{2\cdot \:1},\:x_2=\frac{-3-11}{2\cdot \:1}}$

$--------------------$

$\sf{x=\dfrac{-3+11}{2\cdot \:1}}$

$\sf{x=\dfrac{8}{2\cdot \:1}}$

$\sf{x=\dfrac{8}{2}}$

$\bf{x=4}$

$--------------------$

$\sf{\displaystyle x=\frac{-3-11}{2\cdot \:1}}$

$\sf{x=\dfrac{-14}{2\cdot \:1}}$

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

$\bf{x=-7}$

$--------------------$

The solutions to the quadratic equation are :

$\large\boxed{\sf{x=4,\:x=-7}}$

${\huge{\underline{\small{\mathbb{\pink{HOPE\:HELPS\:UH :)}}}}}}$