%5E2%3D36-square-root-method.jpeg "(x-3)^2=36 Square Root Method")
Solving Quadratic Equations Using the Square Root Method: (x - 3)^2 = 36
The square root method is a useful technique for solving quadratic equations of the form (x + a)^2 = b, where 'a' and 'b' are constants. This method involves isolating the squared term and then taking the square root of both sides. Let's see how it works for the equation (x - 3)^2 = 36.
Step 1: Isolate the Squared Term
The squared term is already isolated on the left-hand side of the equation: (x - 3)^2 = 36
Step 2: Take the Square Root of Both Sides
Taking the square root of both sides of the equation gives us: √((x - 3)^2) = ±√36
Remember to include both the positive and negative square roots of 36, as both will satisfy the equation.
Step 3: Simplify
Simplifying the equation, we get: (x - 3) = ±6
Step 4: Solve for x
Now we have two possible solutions:
-
x - 3 = 6 Adding 3 to both sides: x = 9
-
x - 3 = -6 Adding 3 to both sides: x = -3
Solution
Therefore, the solutions to the equation (x - 3)^2 = 36 are x = 9 and x = -3.
Conclusion
The square root method offers a straightforward way to solve quadratic equations in the form (x + a)^2 = b. By isolating the squared term and taking the square root of both sides, we can easily find the solutions.