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8090 [49]
3 years ago
12

What is the solution of √x-5 = x-11

Mathematics
1 answer:
PIT_PIT [208]3 years ago
4 0
Hey!


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

<em>Original Equation :</em>
\sqrt{x} - 5 = x - 11

<em>New Equation {Added 5 to Both Sides} :</em>
\sqrt{x} =x-6

Now we must square both sides of the equation.

<em>Old Equation :</em>
\sqrt{x} =x-6

<em>New Equation {Changed by Squaring Both Sides} :</em>
x= x^{2} -12x+36

And now we must solve the new equation.

Step 1 - Switch sides
x^{2} -12x+36=x

Step 2 - Subtract x from both sides
x^{2} -12x+36-x=x-x

Step 3 - Simplify
x^{2} -13x+36=0

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

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

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

\frac{13+ \sqrt{25}}{2}

\sqrt{25}=5

\frac{13+5}{2}

\frac{18}{2}

9

\frac{-(-13)- \sqrt{(-13) ^{2} -4*1*36} }{2*1}

4

<em>So, this means that in the equation \sqrt{x} -5=x-11,</em>  x = 9  <em>and  </em>x = 4.

Hope this helps!


- Lindsey Frazier ♥
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