%5E2%3D49-undo-squaring-by.jpeg "(x-9)^2=49 Undo Squaring By")
Solving Equations by Undoing Squaring: (x-9)² = 49
This article will walk you through solving the equation (x-9)² = 49 by undoing the squaring operation.
Understanding the Equation
The equation presents a squared term: (x-9)². This means the expression inside the parentheses, (x-9), has been multiplied by itself. To isolate x, we need to reverse this squaring operation.
Undoing the Squaring
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Take the square root of both sides: The inverse operation of squaring is taking the square root. Applying this to both sides of the equation gives us:
√[(x-9)²] = ±√49
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Simplify: The square root of (x-9)² is simply (x-9). The square root of 49 is 7, but we need to consider both positive and negative solutions. This gives us:
x - 9 = ±7
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Solve for x: We now have two separate equations to solve:
- x - 9 = 7 Adding 9 to both sides gives us x = 16
- x - 9 = -7 Adding 9 to both sides gives us x = 2
Solution
Therefore, the solutions to the equation (x-9)² = 49 are x = 16 and x = 2.
Key Concepts
- Inverse Operations: Every mathematical operation has an inverse. For squaring, the inverse is taking the square root.
- Square Roots: The square root of a number is a value that, when multiplied by itself, equals the original number.
- Positive and Negative Solutions: When undoing squaring, we need to consider both positive and negative solutions because squaring a positive or negative number results in a positive value.