Question

2x² - 7x + 3 = 0 solve the quadratic equations by using the quadratic formula​

Answer 1

x = 3

x =1/2

Explanation:

`2x^2-7x+3=0\\\\x_1 ,2 =(-b\pm √(b^2-4ac))/(2a)\\\\\mathrm{For\:}\quad a=2\\\:b=-7\\,\:c=3\\:\quad x_(1,\:2)=(-\left(-7\right)\pm √(\left(-7\right)^2-4*\:2*\:3))/(2*\:2)\\\\=(7+√(\left(-7\right)^2-4*\:2*\:3))/(2*\:2)\\\\7+√(\left(-7\right)^2-4*\:2*\:3)=7+√(25)\\\\=(7+√(25))/(2*\:2)\\\\=(7+√(25))/(4)\\\\√(25)=5\\\\=(7+5)/(4)\\\\=(12)/(4)\\\\=3 \\`

`x=(-\left(-7\right)-√(\left(-7\right)^2-4*\:2*\:3))/(2*\:2)\\\\=(7-√(\left(-7\right)^2-4*\:2\cdot \:3))/(2*\:2)\\\\7-√(\left(-7\right)^2-4* \:2*\:3)=7-√(25)\\\\=(7-√(25))/(2* \:2)\\\\=(7-√(25))/(4)\\√(25)=5\\\\=(7-5)/(4)\\=(2)/(4)\\\\=(1)/(2)`

Answer 2

x = 1/2 or 3

Explanation:

Compare the given equation to the standard form equation to identify the values of the variables in the formula. Then put those values in the formula and do the arithmetic.

`ax^2+bx+c=0\\\\2x^2-7x+3=0\\\\a=2;\ b=-7;\ c=3\\\\x=(-b\pm√(b^2-4ac))/(2a)\\\\x=(-(-7)\pm√((-7)^2-4(2)(3)))/(2(2))=(7\pm√(25))/(4)=(7\pm 5)/(4)\\\\x=\left\{(1)/(2),3\right\}`