Step-by-step explanation:
[tex] {2x}^{2} + 8x - 1 = 0 \\ {x}^{2} + 4x - \frac{1}{2} = 0 \\ {x}^{2} + 4x + {( \frac{1}{4} )}^{2} - \frac{1}{2} - { (\frac{1}{4} )}^{2} = 0 \\ {(x + \frac{1}{4}) }^{2} - \frac{9}{16} = 0 \\ {(x + \frac{1}{4}) }^{2} = \frac{9}{16} \\ x + \frac{1}{4} = ±( \frac{ 3}{4} ) \\ x = \frac{1}{2} \: or \: - 1[/tex]
Answer:
Step-by-step 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
