4.6 Completing the Square

4.6 COMPLETING THE SQUARE

SOLVING BY FINDING SQUARE ROOTS

Solving equations of the form1. Isolate the variable2. “Undo the Square” by taking the square root

of both sides

Don’t forget: when you take the square root your solution is ±

2ax c

EXAMPLE: SOLVE EACH EQUATION BY FINDING SQUARE ROOTS

24 10 46x

EXAMPLE: SOLVE EACH EQUATION BY FINDING SQUARE ROOTS

23 5 25x

EXAMPLE: SOLVE EACH EQUATION BY FINDING SQUARE ROOTS

23 16 1x Note: No real number squared is equal to – 5, so the equation does not have a real number solution

SOLVING A PERFECT SQUARE TRINOMIAL Remember that a perfect square trinomials

are of the form:

Sometimes they can be set equal to a constant

2 2

2 2

2

2

a ab b

a ab b

SOLVING A PERFECT SQUARE TRINOMIAL

When a perfect square trinomial is set equal to a constant:

1. Factor the trinomial2. Take the square root of both sides3. Solve for the value of the variable

EXAMPLE: SOLVE EACH EQUATION

2 4 4 25x x

EXAMPLE: SOLVE EACH EQUATION

2 14 49 25x x

COMPLETING THE SQUARE

If is part of a perfect square trinomial, we can find a constant c so that

is a perfect square trinomial.

This is a process called completing the square

2x bx2x bx c

COMPLETING THE SQUARE

We can form a perfect square trinomial

from by adding 2x bx

2

2

b

COMPLETE THE SQUARE

1. Find the value of

2. Add the value to the expression, this completes the square

2

2

b

2x bx

EXAMPLE: COMPLETE THE SQUARE

2 6x x

EXAMPLE: COMPLETE THE SQUARE

2 10x x

SOLVING AN EQUATION BY COMPLETING THE SQUARE

1. Rewrite the equation so it is of the form

2. Complete the Square: Add to both sides

3. Factor the prefect square trinomial4. Take the square root of both sides5. Solve for the variable

2x bx c 2

2

b

EXAMPLE: SOLVE EACH EQUATION BY COMPLETING THE SQUARE

EXAMPLE: SOLVE EACH EQUATION BY COMPLETING THE SQUARE

23 12 6 0x x

EXAMPLE: SOLVE EACH EQUATION BY COMPLETING THE SQUARE

22 3 9x x x

HOMEWORK

P 237 #1 – 8, 12 – 45 odd