Question

6x^2+4x-20=0
Solve the equation by factorizing

Answer 1

The final answer is: $x= \frac{(-1\pm\sqrt{31})}{3}$

Step-by-step explanation:

$\ Given \ value:\\\\6x^2+4x-20=0\\\\\ Find:\\\\\ factor = ?\\\\\ Solution:\\\\6x^2+4x-20=0\\\\ \ taking \ common \ a \ value \ that\ is \ 2\\\\\rightarrow 2(3x^2+2x-10)=0\\\\\rightarrow 3x^2+2x-10=0\\\\\ compare \ the \ value \ with \ ax^2+bx+c=0\\\\a= 3\\ b= 2\\c= -10\\\\\ formula:\\\\x= \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\ put \ the \ value \ of \ a, b, c \ in \ given \ equation\\\\x= \frac{-(2)\pm\sqrt{(2)^2-4\times 3 \times (-10)}}{2 \times 3}$

$\rightarrow x= \frac{-2\pm\sqrt{4+120}}{6}\\\\\rightarrow x= \frac{-2\pm\sqrt{124}}{6}$

$\rightarrow x= \frac{-2\pm2\sqrt{31}}{6}\\\\\rightarrow x= \frac{2(-1\pm\sqrt{31})}{6}\\\\\rightarrow x= \frac{(-1\pm\sqrt{31})}{3}$

Learn more:

• Factors: https://brainly.in/question/8919211

Answer 2

♪Given:-

•Equation= 6x²+4x-20=0 [P(x)]

♦To Find:-

The Value of x?

★Proof:-

•Divide P(x) with 2 for Simplification•

→6x²+4x-20=0 –-[÷by 2]-–

→3x²+2x-10=0

S=2

P=-30

*Since there is no Common factor, we will use DISCRIMINANT FORMULA*

→d=b²-4ac

a=3,b=2,c=-10

→d=(2)²-4×3×(-10)

→d=4+120

→d=124

→√d=±√124

→√d=±2√31

$\rule{200}{1}$

•Taking x(+)=$\frac{-b+ \sqrt{d}}{2a}$

→x=$\frac{-2+2 \sqrt{31}}{2×3}$

→x=$\frac{-2+2 \sqrt{31}}{6}$

→x=$\frac{\cancel{2}(-1+ \sqrt{31})}{\cancel{6}}$

→x=$\frac{(-1+ \sqrt{31})}{3}$

$\rule{200}{1}$

•Taking x(-)=$\frac{-b- \sqrt{d}}{2a}$

→x=$\frac{-2-2 \sqrt{31}}{2×3}$

→x=$\frac{-2-2 \sqrt{31}}{6}$

→x=$\frac{\cancel{2}(-1- \sqrt{31})}{\cancel{6}}$

→x=$\frac{(-1- \sqrt{31})}{3}$

$\rule{200}{7}$

→x=$\frac{(-1± \sqrt{31})}{3}$