X^2 + 1/2x + = 2 +
Help please
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Answer:
Step 2:
For Completing the square,
[tex](\frac{1}{2} coefficient\ x)^{2} =(\frac{1}{2}\times \frac{1}{2})^{2}=\frac{1}{16}[/tex]
Add half coefficient of x square on both the side we get
[tex]x^{2}+\dfrac{x}{2}+\frac{1}{16}=2+\frac{1}{16}[/tex]
Step-by-step explanation:
Solve:
[tex]2x^{2}+x-4=0[/tex]
[tex]2x^{2}+x=4[/tex]
Solution:
Step 1:
Dividing both the side by two we get
[tex]x^{2}+\dfrac{x}{2}=2[/tex]
Step 2:
For Completing the square,
[tex](\frac{1}{2} coefficient\ x)^{2} =(\frac{1}{2}\times \frac{1}{2})^{2}=\frac{1}{16}[/tex]
Add half coefficient of x square on both the side we get
[tex]x^{2}+\dfrac{x}{2}+\frac{1}{16}=2+\frac{1}{16}[/tex]
Step 3:
We know [tex](a +b)^{2} = a^{2}+2ab +b^{2}[/tex]
[tex](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}}[/tex]