Finding the missing value to make a perfect square.
by
Steve Larson 7 years ago
- Math
- Algebra
- Quadratic Equations
- Completing the Square
0
7 years ago
- Math
- Algebra
- Quadratic Equations
- Completing the Square
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What if a ≠ 1?
In the example above it is important that the coefficient in front of x2 is equal to 1. What do you do if you are asked to solve a quadratic equation where a ≠ 1? Just apply one of the most frequently used problem-solving techniques in math, namely... transform the problem to one you've already solved 🙃 What does that mean in our context? Just divide your equation by a!
For example: assume we have to solve
2x2 + 12x - 5 = 0by completing the square. We see that a = 2. Dividing either side by 2, we obtain
x2 + 6x - 2.5 = 0and so the coefficient in front of x2 is equal to 1. Now just go ahead with the steps we explained in the example above.
- What if b = 0?
If b=0, then you may skip Steps 2, 3, and 4, and go from x2 = - c (Step 1) directly to x = ±√|c| (Step 5).
Why?
Because in Step 2 we take b and
perform some arithmetic operations on it, which gives us the number with which we will 'complete the square.'
Note that if b = 0, then (b/2)2 = 0, and so we would add 0 to both sides of the equations. This is, of course, redundant.
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Step-by-Step Examples
Algebra
Quadratic Equations
Find the Perfect Square Trinomial
Step 1
Factor out the
Step 2
To find the value , divide the coefficient of by and square the result.
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Multiply the numerator by the reciprocal of the denominator.
Multiply .
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Multiply by .
Multiply by .
Apply the product rule to .
Raise to the power of .
Raise to the power of .
Step 3
Add to get the perfect square trinomial.
Step 4
Simplify.
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Apply the distributive property.
Simplify.
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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
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