Solve for x x-11 square root of x+30=0

Problem

x−11√(,x)+30=0

Solution

1. Identify the equation as being in quadratic form by letting u=√(,x) which implies u2=x

2. Substitute the variable u into the original equation to create a standard quadratic equation.

u2−11*u+30=0

3. Factor the quadratic expression by finding two numbers that multiply to 30 and add to −11

(u−5)*(u−6)=0

4. Solve for u by setting each factor equal to zero.

u−5=0⇒u=5

u−6=0⇒u=6

5. Back-substitute √(,x) for u to find the values of x

√(,x)=5⇒x=5=25

√(,x)=6⇒x=6=36

6. Verify the solutions by plugging them back into the original equation to ensure they are not extraneous.

25−11√(,25)+30=25−55+30=0

36−11√(,36)+30=36−66+30=0

Final Answer

x=25,36

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