Question

Solve for x in the equation

Answer 1

Answer:

Option d is correct

Step-by-step explanation:

$x^2 + 11x + \frac{121}{4} = \frac{125}{4}$

$x^2 + 11x + \frac{121}{4} - \frac{125}{4} = 0$

$x^2 + 11x + \frac{121-125}{4} = 0$

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

Using quadratic formula

$x = \frac{-b +- \sqrt{b^2-4ac}}{2a}$

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

$x = \frac{-11 +- \sqrt{11^2-4(1)(-1)}}{2(1)}$

$x = \frac{-11 +- \sqrt{121+4}}{2}$

$x = \frac{-11 +- \sqrt{125}}{2}$

$x = \frac{-11 +- \sqrt{5*25}}{2}$

$x = \frac{-11 +- 5\sqrt{5}}{2}$

$x = \frac{-11}{2} +- \frac{5\sqrt{5}}{2}$

Answer 2

Answer:

Choice D is correct answer.

Step-by-step 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.