Complete the Square 4x^2+12x+9

Problem

4*x2+12*x+9

Solution

1. Factor out the leading coefficient 4 from the first two terms to isolate the x2 term.

4*(x2+3*x)+9

2. Identify the coefficient of the x term inside the parentheses, which is 3

3. Calculate the value needed to complete the square by taking half of the x coefficient and squaring it.

(3/2)2=9/4

4. Add and subtract this value inside the parentheses.

4*(x2+3*x+9/4−9/4)+9

5. Distribute the 4 to the subtracted term to move it outside the parentheses.

4*(x2+3*x+9/4)−4*(9/4)+9

6. Simplify the constant terms outside the parentheses.

4*(x2+3*x+9/4)−9+9

4*(x2+3*x+9/4)+0

7. Factor the perfect square trinomial inside the parentheses.

4*(x+3/2)2

Final Answer

4*x2+12*x+9=4*(x+3/2)2

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