Question

solve 9x2 - 15x + 1 = 0 by completing the square

Answer 1

9x² - 15x + 1 = 0

Take away 1 from both sides:

9x² - 15x = - 1

Divide both sides by 9 (because we need coefficient of x² to be 1):

x² - 15/9 x = -1/9

add (b/2)² to both sides:

x² - 15/9 x + (15/18)² = -1/9 + (15/18)²

Complete the square:

(x - 15/18)² = 7/12

Simplify 15/18:

(x - 5/6)² = 7/12

Square root both sides:

x - 5/6 = ± √7/12

Add 5/6 to both sides:

x = √7/12 + 5/6 or x = -√7/12 + 5/6

Evaluate:

x = 1.6 or 0.07

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Answer: x = 1.6 or 0.07