Question - Solving Quadratic Equation by Factoring as Difference of Squares
Solution:
The equation provided in the image is:\[100x^2 - 81 = 0\]This equation can be seen as a difference of squares, which takes the form $$a^2 - b^2 = (a+b)(a-b)$$. Applying this to the given equation, we have:\[a^2 = (10x)^2\]\[b^2 = 81\]So the equation can be rewritten as:\[(10x)^2 - 9^2 = 0\]This further breaks down into:\[(10x + 9)(10x - 9) = 0\]Now, we solve each part of the equation separately to find the values of x:1. $$10x + 9 = 0$$\[10x = -9\]\[x = -\frac{9}{10}\]2. $$10x - 9 = 0$$\[10x = 9\]\[x = \frac{9}{10}\]Thus, the two solutions for $$x$$ are $$-\frac{9}{10}$$ and $$\frac{9}{10}$$.
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