Question

Solve for x in the equation

Answer 1

Choice D is correct answer.

Explanation:

We have given a quadratic equation.

x²+11x+121/4 = 125/4

x²+11x+121/4-125/4 = 0

x²+11x+(121-125)/4 = 0

x²+11x+(-4)/4 =0

x²+11x-1 = 0

ax²+bx+c = 0 is general quadratic equation.

Comparing above equations, we have

a = 1 , b = 11 and c = -1

x = (-b±√b²-4ac) / 2a is quadratic formula to solve equation.

x = (-11±√(11)²-4(1)(-1) ) /2(1)

x = (-11±√121+4) / 2

x = (-11±√125) / 2

x = (-11±5√5) / 2

x = -11/2±5√5/2 is the solution of given quadratic equation.

Answer 2

Option d is correct

Explanation:

`x^2 + 11x + (121)/(4) = (125)/(4)`

`x^2 + 11x + (121)/(4) - (125)/(4) = 0`

`x^2 + 11x + (121-125)/(4) = 0`

`x^2 + 11x - 1 = 0`

Using quadratic formula

`x = (-b +- √(b^2-4ac))/(2a)`

from the above equation a = 1 b = 11 c = -1 put these values in the above formula

`x = (-11 +- √(11^2-4(1)(-1)))/(2(1))`

`x = (-11 +- √(121+4))/(2)`

`x = (-11 +- √(125))/(2)`

`x = (-11 +- √(5*25))/(2)`

`x = (-11 +- 5√(5))/(2)`

`x = (-11)/(2) +- (5√(5))/(2)`