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Solving Equations That Have Radical Terms

Part 1

In this video, we are going to solve simple equations containing radical expression.

In \sqrt{x}=7, first square both sides of the equation
\sqrt{x}^2=7^2
x=49

If there are other values in the equation, then first isolate the \sqrt{x} before squaring both sides of the equation.

Part 2

In the second part, we are going to solve more complex equations containing radical expression.

For example:
\sqrt{x}=(x-5)

Square both sides of the equation
\sqrt{x}^2=(x-5)^2

Use FOIL to complete the squaring if necessary
x=(x-5)(x-5)
x=x^2-5x-5x+25

Combine like terms
x=x^2-10x+25

Since it’s a quadratic equation, use the quadratic equation
x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

Substitute the variables
x=\frac{11\pm\sqrt{(-11)^2-4(1)(25)}}{2(1)}
x=\frac{11\pm\sqrt{121-4(1)(25)}}{2(1)}
x=\frac{11\pm\sqrt{21}}{2}

So we have:
x=\frac{11+\sqrt{21}}{2} and x=\frac{11-\sqrt{21}}{2}

In the end, x is approximately 7.8 or 3.2

If it was -7.8 instead of 7.8, then it cannot be a negative answer since the square root of a negative number is imaginary. In this case, the final answer would just be 3.2