X^2 + 1/2x + = 2 + Help please

Question

asked Sep 21, 2020 235k views

1 Answer

Hammythepig · Answer 1 · 2020-09-28T12:35:06+0000

Answer:

Step 2:

For Completing the square,

$((1)/(2) coefficient\ x)^(2) =((1)/(2)* (1)/(2))^(2)=(1)/(16)$

Add half coefficient of x square on both the side we get

Explanation:

Solve:

2x^(2)+x-4=0

2x^(2)+x=4

Solution:

Step 1:

Dividing both the side by two we get

x^(2)+(x)/(2)=2

Step 2:

For Completing the square,

$((1)/(2) coefficient\ x)^(2) =((1)/(2)* (1)/(2))^(2)=(1)/(16)$

Add half coefficient of x square on both the side we get

x^(2)+(x)/(2)+(1)/(16)=2+(1)/(16)

Step 3:

We know
(a +b)^(2) = a^(2)+2ab +b^(2)

$(x+(1)/(4))^(2)=(33)/(16) \\ \\(x+(1)/(4))=\pm \sqrt{(33)/(16)} \\\\x=-(1)/(4)\pm \sqrt{(33)/(16)}$