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Solving the Equation (x + 8)² - 7 = 0
This article will guide you through solving the quadratic equation (x + 8)² - 7 = 0. We'll use a step-by-step approach to find the solutions for 'x'.
1. Isolate the Squared Term:
Begin by isolating the term with the squared variable (x + 8)² on one side of the equation:
(x + 8)² = 7
2. Take the Square Root:
To get rid of the square, take the square root of both sides of the equation. Remember that taking the square root introduces both positive and negative solutions:
√(x + 8)² = ±√7
This simplifies to:
x + 8 = ±√7
3. Solve for x:
Subtract 8 from both sides of the equation to isolate 'x':
x = -8 ±√7
4. The Solutions:
This gives us two solutions for 'x':
- x = -8 + √7
- x = -8 - √7
Therefore, the solutions to the equation (x + 8)² - 7 = 0 are x = -8 + √7 and x = -8 - √7.
Conclusion
By applying algebraic manipulations, we successfully solved the quadratic equation (x + 8)² - 7 = 0, finding its two distinct solutions. This method involves isolating the squared term, taking the square root of both sides, and finally isolating the variable 'x'. Remember that taking the square root always introduces both positive and negative solutions.