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Solving Quadratic Equations by Completing the Square


Solve by completing the square: 3x2 - 30 = -21x


Step 1 Isolate the x2-term and the x-term on one side of the equation.

Add 21x to both sides.

Add 30 to both sides.

 3x2 - 30 = -21x

3x2 + 21x - 30 = 0

3x2 + 21x = 30

Step 2 If the coefficient of x2 is not 1, divide both sides of the equation by the coefficient of x2.

Divide both sides by 3.

 x2 + 7x = 10
Step 3 Find the number that completes the square: Multiply the coefficient of x by . Square the result.

The coefficient of the x-term is 7.

Step 4 Add the result of Step 3 to both sides of the equation.

Add to both sides.

Simplify the right side.

The result is .


Step 5 Write the trinomial as the square of a binomial.
Step 6 Finish solving using the Square Root Property.

Use the Square Root Property.

For each equation, subtract from both sides and simplify the radical.
Step 7 Check each solution. We leave the check for you.  
The solutions of 3x2 - 30 = -21x are


To divide both sides of an equation by 3, we divide each term by 3, like this:

We can use the “plus or minus” symbol to write the solutions like this

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