Question

Solve the equation

2x2 + 8x – 1 = 0
by completing the square.
Give your answers correct to 2 decimal places.

Answer 1

Explanation:

divide each term by 2 to begin with x²

x² + 4x - 1/2 = 0

now add 1 to each side

x² + 4x = 1/2

now divide 4 in half and square the result and add it to each side

x² + 4x + 4 = 1/2 + 4

(x + 2)² = 9/2

Answer 2

Explanation:

`{2x}^(2) + 8x - 1 = 0 \\ {x}^(2) + 4x - (1)/(2) = 0 \\ {x}^(2) + 4x + {( (1)/(4) )}^(2) - (1)/(2) - { ((1)/(4) )}^(2) = 0 \\ {(x + (1)/(4)) }^(2) - (9)/(16) = 0 \\ {(x + (1)/(4)) }^(2) = (9)/(16) \\ x + (1)/(4) = ±( ( 3)/(4) ) \\ x = (1)/(2) \: or \: - 1`