Solving equations by completing the square method, Mathematics

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Eucledian space, examples

examples

Jack 2/12/2013 2:31:28 AM example, Solve by completing the square. i. 3x² = 9x ii. 2x² + 3x + 1 = 0 Solutions i. 3x² = 9x or (3x² - 9x = 0) x² - 3x = 0 (Step 1) x² - 3x + (-(3/2)²) = -(3/2)² (Step 2) x(-(3/2)²)= 9/4 (Step 3) x -3 = + √(9/4) (step 4) (∴ x = (3/2) + (3/2)) = (3+3)/2 or (3/2) - (3/2) = (= 3 or 0) ii) 2x² + 3x + 1 = 0 or (2x² + 3x = -1) X² + (3x/2) = -(1/2) (step 1) X² + (3x/2) + (3/4)²= (3/4)² - 1/2 (step 2) (x +(3/4)²) = 1/16 (step 3) X + (3/4) = + √(1/16) X = - (3/4) = + (1/4) -(3/4) + (1/4) or -(3/4)-(1/4) X = -(1/2) or x = -1

Jack

2/12/2013 2:31:28 AM

example,

Solve by completing the square.

i. 3x² = 9x

ii. 2x² + 3x + 1 = 0

Solutions

i. 3x² = 9x or

(3x² - 9x = 0)

x² - 3x = 0 (Step 1)

x² - 3x + (-(3/2)²) = -(3/2)² (Step 2)

x(-(3/2)²)= 9/4 (Step 3)

x -3 = + √(9/4) (step 4)

(∴ x = (3/2) + (3/2))

= (3+3)/2 or (3/2) - (3/2) =

(= 3 or 0)

ii) 2x² + 3x + 1 = 0 or (2x² + 3x = -1)

X² + (3x/2) = -(1/2) (step 1)

X² + (3x/2) + (3/4)²= (3/4)² - 1/2 (step 2)

(x +(3/4)²) = 1/16 (step 3)

X + (3/4) = + √(1/16)

X = - (3/4) = + (1/4)

-(3/4) + (1/4) or -(3/4)-(1/4)

X = -(1/2) or x = -1

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