Question

50 POINTS!!! Re write the equation by completing the square x^2- 6x - 16 = 0

Answer 1

• (x - 3)² = 25

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Use the identity for the square of a sum:

• (a + b)² = a² + 2ab + b²

Comparing with the given we see that:

• a = x, 2ab = - 6x

Then find b:

• 2bx = - 6x
• b = - 3

To complete the square we need to add b² = (-3)² = 9 to both sides:

• x² - 6x + 9 - 16 = 9
• (x - 3)² - 16 = 9
• (x - 3)² = 25