Solve each radical equation. Check potential solutions. \sqrt{5x}=x-10

Harlen Pritchard

Harlen Pritchard

Answered question

2021-09-29

Solve each radical equation. Check potential solutions.
5x=x10

Answer & Explanation

tabuordg

tabuordg

Skilled2021-09-30Added 99 answers

Step 1
To solve the radical equation, isolate the radical expression and taking square on both sides to solve the equation.
Now the equation becomes quadratic after squaring each side, then solve the quadratic equation by factoring the terms.
To check the potential solution, substitute back the two values of x in the radical equation to check which value of x satisfying the equation.
Step 2
Isolate the radical expression from the equation,
5x=x10
Squaring each side to solve the equation,
5x=(x10)25x=x2+100=20x
x220x5x+100=0
x225x+100=0
x220x5x+100=0
x(x20)5(x20)=0
x=5,20
Now, checking these two values of x by substituting back in the radical equation,
Substituting x=5 in the left hand side of the radical equation to check,
5x+10
=5×5+10
=25+10
=5+10
=15
Since the right hand side of radical equation is x=5, which is not equal to L.H.S which is 15, so x=5 is not the solution of this equation.
Substituting x=20 in the equation to check,
5x+10
=5×20+10
=100+10
=10+10
=20
Since the R.H.S of equation is x which is 20, so L.H.S is equal to the R.H.S, so x=20 is the solution of the radical equation.

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