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