Question

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

Accepted Answer

First solve the Square root of (16+x^2)2x + (4 + x) = 11Remove parenthesis around (4 + x)2x + 4 + x = 11Reorder the terms:4 + 2x + x = 11Combine like terms: 2x + x = 3x4 + 3x = 11Solving4 + 3x = 11Solving 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 + -4Combine like terms: 4 + -4 = 00 + 3x = 11 + -43x = 11 + -4Combine like terms: 11 + -4 = 73x = 7Divide each side by '3'.x = 2.333333333

Answer

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.

Answer

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.

Math

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

Expert Answers

We’ll help your grades soar

Related Questions

solve the equation: 2^(2x-1)= 8^x

Solve for x sqrt(2x+5) = sqrt(x+2) + sqrt(2x-3).

`arcsin(sqrt(2x)) = arccos(sqrt(x))` Solve the equation for x

Solve the equation sec^2x - 2 tan x = 4

Solve the equation: |3x+2|=|3-2x|Solve the equation: |3x+2|=|3-2x|