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Chapter: Quadratic Equations· Mathematics Part 1 (Algebra)

Complete the following activity to solve \(x^2 - 10x + 9 = 0\) by completing the square method.\(x^2 - 10x + 9 = 0\)\(\therefore x^2 - 10x + \) ____ \( - 25 + 9 = 0\)\(\therefore (x - \) ____ \()^2 = \) ____\(\therefore x - 5 = 4\) or \(x - 5 = \) __…

Complete the following activity to solve \(x^2 - 10x + 9 = 0\) by completing the square method.

\(x^2 - 10x + 9 = 0\)
\(\therefore x^2 - 10x + \) ____ \( - 25 + 9 = 0\)
\(\therefore (x - \) ____ \()^2 = \) ____
\(\therefore x - 5 = 4\) or \(x - 5 = \) ____
\(\therefore x = \) ____ or \(x = 1\)

1 answer

Best answer

Answer: 25; \((x - 5)^2 = 16\); \(-4\); \(x = 9\) or \(x = 1\)

Third term needed \(= \left(\dfrac{1}{2} \times 10\right)^2 = 25\).

\(x^2 - 10x + 25 - 25 + 9 = 0\)

\((x - 5)^2 - 16 = 0 \Rightarrow (x - 5)^2 = 16\)

\(x - 5 = 4\) or \(x - 5 = -4\)

\(x = 9\) or \(x = 1\)

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