%5E2%3D40.jpeg "(x-5)^2=40")
Solving the Equation (x - 5)^2 = 40
This equation involves a squared term, which requires us to use the square root property to solve for 'x'. Here's a step-by-step solution:
1. Isolate the Squared Term
The equation is already in this form.
2. Take the Square Root of Both Sides
Remember that taking the square root of a number gives both a positive and negative solution.
√((x - 5)²) = ±√40
3. Simplify
x - 5 = ±√40
4. Isolate 'x'
Add 5 to both sides of the equation:
x = 5 ± √40
5. Simplify the Radical
√40 can be simplified as √(4 * 10) = 2√10
6. Final Solution
Therefore, the solutions for the equation (x - 5)² = 40 are:
- x = 5 + 2√10
- x = 5 - 2√10
Explanation:
The equation represents a quadratic equation, and its solutions are the points where the parabola represented by the equation intersects the x-axis. The solutions we found are the two x-intercepts.