Raise each side of the equation to the reciprocal of the rational exponent.
x=5
Practice makes perfect
To solve equations with a variable expression raised to a rational exponent, we raise each side of the equation to the reciprocal of the rational exponent.
x^(m n)=k ⇔ (x^(m n))^() n m=k^() n m
Remember, if m is even, then (x^(m n))^() n m=|x|.
In this case m= 1, so we do not need to worry about this. Let's 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 the equation. Let's determine a, b, and c.
x^2+2x-35=0 ⇔ 1x^2+ 2x+( - 35)=0
We see above that a= 1, b= 2, and c= - 35. 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=- 2± 12/2
x=- 2-12/2
x=- 2+12/2
x=- 7
x=5
Checking the Solutions
Next, we will check the solutions by substituting - 7 and 5 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 - 7.
