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Solving a square root equation might seem tricky at first, but it becomes quite straightforward once you understand the key steps. These types of equations have a variable within a square root which you need to solve. The main goal is to eliminate the square root, which allows you to isolate and determine the value of the variable.
One effective way to eliminate the square root sign is to square both sides of the equation. For example, given the equation \(\sqrt{6x+19}=7\), squaring both sides removes the square root, leaving you with \(6x + 19 = 49\).
Remember, whenever you square a square root, you simply "free" what's inside of it. This technique is essential for turning a square root equation into a more familiar linear equation.

It's crucial to check whether the solution you find actually satisfies the original equation. Sometimes squaring can introduce what are known as extraneous solutions, which make the left side equal to the right side of the squared equation but not the original.
To verify a solution, substitute the value you found back into the original equation. For the equation \(\sqrt{6x+19}=7\), check by substituting \(x = 5\) back in: \(\sqrt{6*5 + 19}\).
Simplify your calculation: \(6*5 + 19 = 49\), and the square root of 49 is indeed 7, which equals the right-hand side of the equation. This confirms that \(x = 5\) is a true solution.

Isolating variables in an equation is a critical process that enables you to solve for the unknowns. In our equation \(6x + 19 = 49\), isolate \(x\) by performing arithmetic operations that keep the equation balanced.
First, you subtract 19 from both sides to get \(6x = 30\). This step "moves" the 19 out of the way, simplifying the expression on one side of the equation.
Then, divide both sides by 6. This step isolates \(x\) even further, giving you \(x = 5\). These operations are part of a methodical approach that allows you to simplify and solve equations step-by-step.