# Solving quadratic equations by completing the square

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##### Intros

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##### Examples

###### Lessons

**Solving a quadratic equation with TWO REAL SOLUTIONS**

Solve by completing the square: $x^2+10x+6=0$**Solving a quadratic equation with ONE (REPEATED) REAL SOLUTION**

Solve by completing the square: $9x^2+25=30x$**Solving a quadratic equation with TWO COMPLEX SOLUTIONS**

Solve by completing the square: $-3x^2-24x=49$

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###### Topic Notes

When a quadratic equation cannot be factorized, we can use the method of completing the square to solve the equation.

4-step approach:

1. isolate X's on one side of the equation

2. factor out the

3. "completing the square"

• X-side: inside the bracket, add (half of the coefficient of $X)^2$

• Y-side: add [

4. clean up

• X-side: convert to perfect-square form

• Y-side: clean up the algebra

1. isolate X's on one side of the equation

2. factor out the

*of $X^2$*__leading coefficient__3. "completing the square"

• X-side: inside the bracket, add (half of the coefficient of $X)^2$

• Y-side: add [

*$\cdot$ (half of the coefficient of $X)^2$ ]*__leading coefficient__4. clean up

• X-side: convert to perfect-square form

• Y-side: clean up the algebra

###### Basic Concepts

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videos

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