(5x-2)^2=10

Jasonbradley

2 min read Jun 16, 2024

Solving the Equation: (5x-2)^2 = 10

This article will guide you through the steps of solving the equation (5x-2)^2 = 10.

Step 1: Square Root Both Sides

To eliminate the square, take the square root of both sides of the equation:

√(5x - 2)^2 = ±√10

This gives us:

5x - 2 = ±√10

Step 2: Isolate the Variable

Now, isolate the variable 'x' by performing the following operations:

Add 2 to both sides:

5x = 2 ± √10
Divide both sides by 5:

x = (2 ± √10)/5

Step 3: Simplify the Solution

The solution for 'x' is:

x = (2 + √10)/5 or x = (2 - √10)/5

These are the two possible solutions for the equation (5x-2)^2 = 10.

Conclusion

By following the steps outlined above, we have successfully solved the quadratic equation (5x-2)^2 = 10. The solutions for 'x' are (2 + √10)/5 and (2 - √10)/5.