Question

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

Answer 1

Answer:

Step 2:

For Completing the square,

$(\frac{1}{2} coefficient\ x)^{2} =(\frac{1}{2}\times \frac{1}{2})^{2}=\frac{1}{16}$

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

$x^{2}+\dfrac{x}{2}+\frac{1}{16}=2+\frac{1}{16}$

Step-by-step explanation:

Solve:

$2x^{2}+x-4=0$

$2x^{2}+x=4$

Solution:

Step 1:

Dividing both the side by two we get

$x^{2}+\dfrac{x}{2}=2$

Step 2:

For Completing the square,

$(\frac{1}{2} coefficient\ x)^{2} =(\frac{1}{2}\times \frac{1}{2})^{2}=\frac{1}{16}$

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

$x^{2}+\dfrac{x}{2}+\frac{1}{16}=2+\frac{1}{16}$

Step 3:

We know $(a +b)^{2} = a^{2}+2ab +b^{2}$

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