Question

m²-5m=-3 Solve this quadratic equation by completing the square method.

Answer 1

m² - 5m = -3
m² - 2(m)(5)/2 + (5/2)² - (5/2)² = -3
(m - 5/2)² - 25/4 = -3
(m - 5/2)² = (25 - 12)/4
(m - 5/2)² = 13/4
(m - 5/2) = $\frac{+}{}$√13/2

taking (+ve)

m = (√13 + 5)/2

taking (-ve)

m = (-√13 + 5)/2

Answer 2

Given Quadratic equation is

m² -5m = -3

=> m² - 2 × m × 5/2 = -3

=> m²- 2m(5/2)+(5/2)² = -3+(5/2)²

=> ( m - 5/2 )² = -3 + 25/4

=> ( m - 5/2 )² = ( -12 + 25 )/4

=> ( m - 5/2 )² = 13/4

=> m - 5/2 = ± √ ( 13/4 )

m = 5/2 ± √13/2

m = ( 5 + √13 )/2 or

m = ( 5 - √13 )/2

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