Solve the equation 2x + sqrt(16+x^2)=11.

Expert Answers
marilynn07 eNotes educator| Certified Educator
First solve the Square root of (16+x^2)
2x + (4 + x) = 11

Remove parenthesis around (4 + x)
2x + 4 + x = 11

Reorder the terms:
4 + 2x + x = 11

Combine like terms: 2x + x = 3x
4 + 3x = 11

Solving
4 + 3x = 11

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + 3x = 11 + -4

Combine like terms: 4 + -4 = 0
0 + 3x = 11 + -4
3x = 11 + -4

Combine like terms: 11 + -4 = 7
3x = 7

Divide each side by '3'.
x = 2.333333333
malkaam | Student

2x + sqrt(16+x^2)=11

In order to solve this we must first solve the sqrt part

2x + sqrt(16+x^2)=11

2x + 4+x= 11

After that x should be isolated in order to solve the equation

3x +4-4=11-4        (subtracting 4 from both sides)

3x =7

3x/3 =7/3              (dividing both sides by 3)                 

 x =2.33 Answer.

neela | Student

2x+sqrt(16+x^2)=11.

To solve for x, we proceed as below:

sqrt(16+x^2)=11-2x. Square both sides

16+x^2=(11-2x)^2

16+x^2=121-44x+4x^2 . Subtracact 16+x^2 from both sides then,

0=121-22x+4x^2-16-x^2.  Reorder , collect similar terms .

0=121-16-44x+4x^2-x^2.

0=105-44x+3x^2.

3x^2-44x+105 =0 is a quadratic equation . Factorise to solve for x.

3x^2-35x-9x+105=0

x(3x-35)-3(3x-35)=0

(x-3)(3x-35)=0. Equate each factor to zero to get asolution for x.

x-3=0 or 3x=35.

x=3 or x=35/3.

Check:

x=3 is solution that satisfies the equation as,

2(3)+sqrt(16+3^2) =6+sqrt25 =6+5=11 and that is 11 on right .Agreeing.

2(35/3)+sqrt(16+(35/3)^2)=23.333+20.599 4343.932 is not equal to  roght side which is 11 . Hence this is extraneous root.

 

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