Question

Solve for x in the equation x squared + 11 x + StartFraction 121 Over 4 EndFraction = StartFraction 125 Over 4 EndFraction.
x = negative 11 plus-or-minus StartFraction 25 Over 2 EndFraction
x = negative eleven-halves plus-or-minus StartFraction 25 Over 2 EndFraction
x = negative 11 plus-or-minus StartFraction 5 StartRoot 5 EndRoot Over 2 EndFraction
x = negative eleven-halves plus-or-minus StartFraction 5 StartRoot 5 EndRoot Over 2 EndFraction

Answer 1

Answer:

D. x = negative eleven-halves plus-or-minus StartFraction 5 StartRoot 5 EndRoot Over 2 EndFraction

Step-by-step explanation:

Answer 2

The solution of the equation will be x = - 11/2 ± 5√5/ 2. Then the correct option is D.

What is the solution of the quadratic equation by formula method?

The quadratic equation is given as ax² + bx + c = 0.

Then the solution is given as

$\rm x = \dfrac{-b\pm \sqrt{b^2 - 4ac}}{2a}$

The quadratic equation is given below.

x² + 11x + 121/4 = 125/4

  x² + 11x + – 1 = 0

Comparing with the standard equation, we have

a = 1, b = 11, and c = –1

Then the roots of the equation will be

$\rm x = \dfrac{-11\pm \sqrt{11^2 - 4*1*(-1)}}{2*1}\\\\\\\rm x = \dfrac{-11 \pm \sqrt{121 +4}}{2}\\\\\\\rm x = \dfrac{-11\pm \sqrt{125}}{2}\\\\\\x = \dfrac{-11}{2}\pm \dfrac{5\sqrt{5}}{2}$

Then the correct option is D.

More about the solution of the quadratic equation link is given below.

https://brainly.com/question/17376136

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