Raise each side of the equation to a power equal to the index of the radical to eliminate the radical.
Solve the resulting equation. Remember to check your results!
Now we can analyze the given radical equation.
sqrt(2x+30)=x+3Notice that in this equation there is an isolated radical with index equal to 2 on the left-hand side. Then, we will raise each side of the equation to the power of 2.
We obtained a quadratic equation. There are many ways to solve a quadratic equation. We will use the Quadratic Formula to solve this equation. Let's determine a, b, and c.
x^2+4x-21=0 ⇔ 1x^2+ 4x+( - 21)=0
We see above that a= 1, b= 4, and c= - 21. Let's substitute these values into the Quadratic Formula to solve the equation.
Now we can calculate the first root using the positive sign and the second root using the negative sign.
x=- 4± 10/2
x=- 4+10/2
x=- 4-10/2
x=3
x=- 7
Checking the Solutions
Next, we will check the solutions by substituting 3 and - 7 for x into the original equation. If the substitution produces a true statement, we know that our answer is correct. If it does not, then it is an extraneous solution. Let's first check the 3.
