Solve for x x+ square root of x=72

Problem

x+√(,x)=72

Solution

1. Substitute a new variable to simplify the equation by letting u=√(,x) which implies u2=x

2. Rewrite the original equation in terms of u to form a quadratic equation.

u2+u=72

3. Rearrange the equation into standard quadratic form by subtracting 72 from both sides.

u2+u−72=0

4. Factor the quadratic expression by finding two numbers that multiply to −72 and add to 1

(u+9)*(u−8)=0

5. Solve for u by setting each factor to zero.

u=−9

u=8

6. Back-substitute u=√(,x) to find the values of x Since the principal square root √(,x) cannot be negative, we discard u=−9

√(,x)=8

7. Square both sides of the valid equation to solve for x

x=8

x=64

Final Answer

x=64

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