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Solving the Equation: (x-7)² - 4 = (x+1)²
This article will guide you through the process of solving the equation (x-7)² - 4 = (x+1)².
Expanding the Equation
The first step is to expand the squares on both sides of the equation. We can do this using the FOIL method (First, Outer, Inner, Last):
- (x-7)² = (x-7)(x-7) = x² - 7x - 7x + 49 = x² - 14x + 49
- (x+1)² = (x+1)(x+1) = x² + x + x + 1 = x² + 2x + 1
Now, substitute these expanded terms back into the original equation:
x² - 14x + 49 - 4 = x² + 2x + 1
Simplifying the Equation
Next, we simplify the equation by combining like terms:
x² - 14x + 45 = x² + 2x + 1
Subtracting x² from both sides:
-14x + 45 = 2x + 1
Subtracting 2x from both sides:
-16x + 45 = 1
Subtracting 45 from both sides:
-16x = -44
Solving for x
Finally, we isolate x by dividing both sides by -16:
x = -44 / -16
x = 11/4
Conclusion
Therefore, the solution to the equation (x-7)² - 4 = (x+1)² is x = 11/4.