To complete the square for the equation \(x^{2}+2x-3 = 0\), we first want to isolate the quadratic and linear terms on one side.
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Start with the original equation: \[ x^{2} + 2x - 3 = 0 \]
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Move the constant term to the other side: \[ x^{2} + 2x = 3 \]
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Next, complete the square for the left-hand side. To do this, take the coefficient of \(x\) (which is 2), divide it by 2 (to get 1), and then square it (to get 1): \[ \left(\frac{2}{2}\right)^{2} = 1 \]
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Add this square to both sides: \[ x^{2} + 2x + 1 = 3 + 1 \] \[ x^{2} + 2x + 1 = 4 \]
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The left-hand side can now be factored: \[ (x + 1)^{2} = 4 \]
Thus, the completed square form of the equation is: \[ (x + 1)^{2} = 4 \]
So, in answer to the prompt, we fill in the blanks as follows: \[ (x + 1)^2 = 4 \]
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