Respuesta :

Hey!


To solve x in this equation we must first add five to both sides to get [tex] \sqrt{x} [/tex] on its own.

Original Equation :
[tex] \sqrt{x} - 5 = x - 11[/tex]

New Equation {Added 5 to Both Sides} :
[tex] \sqrt{x} =x-6[/tex]

Now we must square both sides of the equation.

Old Equation :
[tex] \sqrt{x} =x-6[/tex]

New Equation {Changed by Squaring Both Sides} :
[tex]x= x^{2} -12x+36[/tex]

And now we must solve the new equation.

Step 1 - Switch sides
[tex] x^{2} -12x+36=x[/tex]

Step 2 - Subtract x from both sides
[tex] x^{2} -12x+36-x=x-x[/tex]

Step 3 - Simplify
[tex] x^{2} -13x+36=0[/tex]

Now we need to solve the rest of the equation using the quadratic formula.

[tex] \frac{-(-13)+ \sqrt{(-13) ^{2}-4*1*36 } }{2*1} [/tex]

[tex]{13+ \sqrt{(-13)^{2}-4*1*36 }=13+ \sqrt{25}[/tex]

[tex] \frac{13+ \sqrt{25}}{2} [/tex]

[tex] \sqrt{25}=5 [/tex]

[tex] \frac{13+5}{2} [/tex]

[tex] \frac{18}{2} [/tex]

9

[tex] \frac{-(-13)- \sqrt{(-13) ^{2} -4*1*36} }{2*1} [/tex]

4

So, this means that in the equation [tex] \sqrt{x} -5=x-11[/tex],  x = 9  and  x = 4.

Hope this helps!


- Lindsey Frazier ♥

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