Question

solve for x.√(4x+9)+x=9.​

Answer 1

ANSWER:

Given:

• √(4x + 9) + x = 9

To Do:

• Solve for x

Solution:

We are given that,

$\implies\sqrt{4x+9}+x=9$

Transposing x to RHS,

$\implies\sqrt{4x+9}=9-x$

Squaring both sides,

$\implies(\sqrt{4x+9})^2=(9-x)^2$

We know that,

⟹ (a - b)^2 = a^2 + b^2 - 2ab

So,

$\implies(\sqrt{4x+9})^2=(9-x)^2$

$\implies4x+9=(9)^2+(x)^2-2(9)(x)$

$\implies4x+9=81+x^2-18x$

Transposing LHS to RHS,

$\implies0=81+x^2-18x-4x-9$

$\implies0=x^2-22x+72$

$\implies x^2-22x+72=0$

Splitting the middle term,

$\implies x^2-18x-4x+72=0$

So,

$\implies x(x-18)-4(x-18)=0$

$\implies (x-18)(x-4)=0$

Hence,

⟹ x = 4 and x = 18

But, this isn't our answer. This is so, because while solving, we squared the terms, due to which one extra solution is obtained.

Therefore, we will see which solution satisfies the given equation, and the one satisfying will be our answer.

So,

For x = 4

$\implies\sqrt{4x+9}+x=9$

Solving LHS,

$\implies\sqrt{4(4)+9}+4$

So,

$\implies\sqrt{16+9}+4$

$\implies\sqrt{25}+4$

$\implies5+4$

$\implies9$

Hence,

$\implies9=9$

As, LHS = RHS, x = 4, is our answer.

For surety, we will check x = 18, too.

For x = 18

$\implies\sqrt{4x+9}+x=9$

Solving LHS,

$\implies\sqrt{4(18)+9}+18$

So,

$\implies\sqrt{72+9}+18$

$\implies\sqrt{81}+18$

$\implies9+18$

$\implies27$

Hence,

$\implies27\neq9$

As, LHS ≠ RHS, x = 18, is not our answer.

Therefore, x = 4, is the final answer.