(x-8)^2-7=25

Jasonbradley

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Jun 17, 2024

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Solving the Equation: (x - 8)² - 7 = 25

This article will guide you through the steps of solving the equation (x - 8)² - 7 = 25.

1. Isolate the Squared Term

To begin, we need to isolate the term with the squared variable. We can do this by adding 7 to both sides of the equation:

(x - 8)² - 7 + 7 = 25 + 7

This simplifies to:

(x - 8)² = 32

2. Take the Square Root

Now, we take the square root of both sides to get rid of the square:

√(x - 8)² = ±√32

This gives us:

x - 8 = ±√32

3. Simplify and Solve for x

Simplify the radical and solve for x:

x - 8 = ±4√2

x = 8 ± 4√2

Therefore, the solutions to the equation (x - 8)² - 7 = 25 are:

x = 8 + 4√2 and x = 8 - 4√2