%5E2%2B2%3D-10-square-root-method.jpeg "(x+3)^2+2=-10 Square Root Method")
Solving (x+3)^2 + 2 = -10 using the Square Root Method
The square root method is a handy technique for solving quadratic equations that are in a specific form:
(x + a)^2 = b
Let's see how to apply this method to the equation:
(x + 3)^2 + 2 = -10
1. Isolate the squared term:
- Subtract 2 from both sides: (x + 3)^2 = -12
2. Apply the square root property:
- Take the square root of both sides, remembering to include both positive and negative solutions: x + 3 = ±√(-12)
3. Simplify the radical:
- Recall that the square root of a negative number is an imaginary number, denoted by 'i': x + 3 = ±2√3i
4. Solve for x:
- Subtract 3 from both sides: x = -3 ± 2√3i
Solution:
Therefore, the solutions to the equation (x+3)^2 + 2 = -10 are:
- x = -3 + 2√3i
- x = -3 - 2√3i
Important Note: This equation has complex solutions because the expression under the square root was negative.
Key Takeaways:
- The square root method is effective for solving quadratic equations in a specific form.
- Remember to include both positive and negative solutions when taking the square root.
- Complex solutions arise when working with negative values under the square root.