%5E2-6%3D43.jpeg "(x+5)^2-6=43")
Solving the Equation (x+5)² - 6 = 43
This article will guide you through the steps of solving the equation (x+5)² - 6 = 43. We'll break down the problem into manageable steps and explain each step in detail.
1. Isolate the Squared Term
Our first goal is to isolate the term (x+5)². To do this, we'll add 6 to both sides of the equation:
(x+5)² - 6 + 6 = 43 + 6
This simplifies to:
(x+5)² = 49
2. Take the Square Root of Both Sides
Now we have a squared term isolated. To get rid of the square, we'll take the square root of both sides of the equation:
√(x+5)² = ±√49
Remember to include both positive and negative roots, as squaring both positive and negative values results in a positive value.
This simplifies to:
(x + 5) = ±7
3. Solve for x
We now have two separate equations to solve:
- x + 5 = 7
- x + 5 = -7
Solving the first equation:
x + 5 - 5 = 7 - 5
x = 2
Solving the second equation:
x + 5 - 5 = -7 - 5
x = -12
4. Solutions
Therefore, the solutions to the equation (x+5)² - 6 = 43 are:
x = 2 and x = -12