Question

find the roots of the following quadratic equation if they exist by the method of completing square

$2 x ^{2} + x - 4 = 0$
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Answer 1

Step-by-step explanation:

The quadratic equation in the previous page's last example was:

(x – 2)2 – 12 = 0

The expression on the left-hand side of this equation can be multiplied out and simplified to be:

x2 – 4x – 8

But we still would not have been able to solve the equation, even with the quadratic formatted this way, because it doesn't factor and it isn't ready for square-rooting

The only reason we could solve it on the previous page was because they'd already put all the x stuff inside a square, so we could move the strictly-numerical portion of the equation to the other side of the "equals" sign and then square-root both sides. They won't always format things as nicely as this. So how do we go from a regular quadratic like the above to an equation that is ready to be square-rooted?

We will have to "complete the square"

THIS MAY HELP U UNDERSTAND