Question

Solve 2x^2 + x - 4 = 0
X2 +

Answer 1

`\large \boxed{\sf \ \ x = -(√(33)+1)/(4) \ \ or \ \ x = (√(33)-1)/(4) \ \ }`

Explanation:

Hello, please find below my work.

`2x^2+x-4=0\\\\\text{*** divide by 2 both sides ***}\\\\x^2+(1)/(2)x-2=0\\\\\text{*** complete the square ***}\\\\x^2+(1)/(2)x-2=(x+(1)/(4))^2-(1^2)/(4^2)-2=0\\\\\text{*** simplify ***}\\\\(x+(1)/(4))^2-(1+16*2)/(16)=(x+(1)/(4))^2-(33)/(16)=0`

`\text{*** add } (33)/(16) \text{ to both sides ***}\\\\(x+(1)/(4))^2=(33)/(16)\\\\\text{**** take the root ***}\\\\x+(1)/(4)=\pm (√(33))/(4)\\\\\text{*** subtract } (1)/(4) \text{ from both sides ***}\\\\x = -(1)/(4) -(√(33))/(4) \ \ or \ \ x = -(1)/(4) +(√(33))/(4)`

Hope this helps.

Do not hesitate if you need further explanation.

Thank you