Completing the Square: Another Example (2.4.3) Flashcards
• When a square term has a coefficient other than 1, divide the entire equation by that coefficient to eliminate having to consider it with the squared term.
• When a square term has a coefficient other than 1, divide the entire equation by that coefficient to eliminate having to consider it with the squared term.
Next, move the constant term to the right side of the equal sign. This allows you to complete the square for the terms remaining on the left side.
To complete the square:
- Divide the coefficient of the unsquared term, the 2 in this example, in half: 2/2 = 1.
- Square that half: (1)2 = 1.
- Add that newly found number to both sides of the
equation: add 1 to both sides.
Now, rewrite the left side as the square of a binomial.
Once you’ve got a square on the left, just take the square root of both sides to get to x.
Then move the constant with x to the right side. And, you’ve indicated your two answers with the ± sign, so you’re done, almost.
Remember: Most people dislike radicals in the denominator.
So, take the extra step to eliminate those from your answers.
And here are your two finished answers.
Next, move the constant term to the right side of the equal sign. This allows you to complete the square for the terms remaining on the left side.
To complete the square:
- Divide the coefficient of the unsquared term, the 2 in this example, in half: 2/2 = 1.
- Square that half: (1)2 = 1.
- Add that newly found number to both sides of the
equation: add 1 to both sides.
Now, rewrite the left side as the square of a binomial.
Once you’ve got a square on the left, just take the square root of both sides to get to x.
Then move the constant with x to the right side. And, you’ve indicated your two answers with the ± sign, so you’re done, almost.
Remember: Most people dislike radicals in the denominator.
So, take the extra step to eliminate those from your answers.
And here are your two finished answers.
