Question

√2x-7+X= 5 Solve the equation with work shown below

Answer 1

Answer:

$x=12(\sqrt2-1)$

Step-by-step explanation:

The given equation is :

$\sqrt{2} x-7+x=5$

Add 7 to both sides of the equation.

$\sqrt{2} x-7+x+7=5+7\\\\\sqrt{2} x+x=12$

Taking x common from both sides of the equation.

$x(\sqrt{2} +1)=12\\\\x=\dfrac{12}{\sqrt2+1}$

Multiplying both numerator and denominator by $\sqrt2-1$

$x=\dfrac{12}{\sqrt2+1}\times \dfrac{\sqrt2-1}{\sqrt2-1}\\\\=\dfrac{12(\sqrt2-1)}{2-1}\\\\=12(\sqrt2-1)$

Hence, the value of x is $12(\sqrt2-1)$.