Find the missing value to complete the square calculator

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

by completing the square. We see that a = 2. Dividing either side by 2, we obtain

and 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 .

Tap for more steps...

Factor out of .

Cancel the common factor.

Rewrite the expression.

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