Question

Find the values of x if square root of √2x+9+x=13

Answer 1

Step-by-step explanation:

√2x+9+x=13

√2x+x+9-13=0

√3x-4=0

√3x=4

x=4\√3

Answer 2

Answer:

$\Large\boxed{X=\frac{160}{3}=53.3 }$

Step-by-step explanation:

Given:

√2x+9+x=13

To find the value of x, first you have to isolate by the x on one side of the equation of square root.

Solutions:

First, you have to used the square from both sides.

$\displaystyle (\sqrt{2x+9+x)^2}=13^2$

Expand by using the distributive property.

$\Large\boxed{\textnormal{Distributive property}}$

$\displaystyle a(b+c)=ab+ac$

Used radical rule.

$\Large\boxed{\textnormal{RADICAL RULES FORMULA}}$

$\displaystyle \sqrt{B=B^\frac{1}{2}}$

Rewrite the problem down.

$\displaystyle ((2x+9+x)^\frac{1}{2})^2$

Used exponent rule.

$\Large\boxed{\textnormal{EXPONENT RULES FORMULA}}}$

$\displaystyle (A^B)^C=A^B^C$

$(2x+9+x)^\frac{1}{2}^2$

Solve.

$\displaystyle \frac{1}{2}*2$

$\displaystyle \frac{1*2}{2}=\frac{2}{2}=1$

$\displaystyle 2x+9+x$

Add. (refine.)

$\displaystyle 2x+x=3x$

$\displaystyle 3x+9$

Solve with exponent.

$\displaystyle 13^2=13*13=169$

$\displaystyle 3x+9=169$

Subtract by 9 from both sides.

$\displaystyle 3x+9-9=169-9$

Solve.

Subtract the numbers from left to right.

$\displaystyle 169-9=160$

$\displaystyle 3x=160$

Then, you divide by 3 from both sides.

$\displaystyle \frac{3x}{3}=\frac{160}{3}$

Solve.

$\displaystyle \boxed{x=\frac{160}{3}}$

Divide numbers from left to right.

$\displaystyle 160\div3=\boxed{53.3}$

$\Large\boxed{X=\frac{160}{3}=53.3 }$

As a result, the correct answer is x=160/3=53.3.