Solve by Factoring square root of 5x+29=x+3

Problem

√(,5*x+29)=x+3

Solution

1. Square both sides of the equation to eliminate the radical.

√(,5*x+29)2=(x+3)2

5*x+29=x2+6*x+9

2. Rearrange the equation into standard quadratic form a*x2+b*x+c=0 by subtracting 5*x and 29 from both sides.

0=x2+6*x−5*x+9−29

x2+x−20=0

3. Factor the quadratic expression by finding two numbers that multiply to −20 and add to 1

(x+5)*(x−4)=0

4. Apply the zero product property to find the potential solutions for x

x+5=0⇒x=−5

x−4=0⇒x=4

5. Check for extraneous solutions by substituting the values back into the original equation.

For *x=−5:√(,5*(−5)+29)=√(,4)=2≠−5+3

For *x=4:√(,5*(4)+29)=√(,49)=7=4+3

Final Answer

√(,5*x+29)=x+3⇒x=4

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