(x-1)(x+2)=4 Please help?

x² + 2x - x - 2 = 4

x² + 1/2x = 6 + (1/2)²

x² + 1/2x = (24 + 1)/4

(x + 1/2)² = 25/4

x + 1/2 = ± 5/2

x = (5 - 1)/2, x = 4/2, x = 2

x = (- 5 - 1)/2, x = - 6/2, x = - 3

Answer: x = 2, - 3

Check:

(2 - 1)(2 + 2) = (- 3 - 1)(- 3 + 2)

1(4) = - 4(- 1)

4 = 4

(x - 1) * (x + 2) = 4

First, FOIL, so this adds the products of the First, Outer, Inner, and Last elements. Doing this we have:

F = x * x = x^2

O = x * 2 = 2x

I = -1 * x = -x

L = -1 * 2 = -2

So, x^2 + 2x - x - 2 = 4

Now, regroup the 2x and -x to just x:

x^2 + x - 2 = 4

Subtract 4 from each side to get the quadratic into standard form:

x^2 + x - 6 = 0

Now, factor. We need the factors of -6 that add to 1 (because + x has a coefficient of 1). These are -2 and 3:

(x - 2) * (x + 3) = 0

Solve each separately, because if either is 0 the product is 0:

x - 2 = 0 means x = 2

x + 3 = 0 means x = -3

So, the solutions (as you found) are x = 2 and x = -3, and there's no way your instructor can complain about this method!

(x - 1)(x + 2) = 4

x² + x - 2 = 4 {used foil method}

x² + x - 6 = 0 {subtracted 4 from both sides}

(x + 3)(x - 2) = 0 {factored into two binomials}

x + 3 = 0 or x - 2 = 0 {set each factor equal to 0}

x = -3 or x = 2 {solved each equation for x}

Give the best answer to Jon Agruda below, he has "the other way"

http://www.algebrahouse.com/

(x-1)(x+2)=4

x^2 - x + 2x - 2 = 4 ..... multiply the two binomials giving

x^2 + x - 2 = 4 .......... now subtract 4 from both sides giving

x^2 + x - 6 = 0 now factor

(x - 2)(x + 3) = 0 and solve separately

x - 2 = 0, x = 2

x + 3 = 0, x = -3

x-1=4 then x=5

or

x+2=4 then x=2

check,

(5-1)(5+2)=4*7=28

(2-1)(2+2)=1*4=4

This is the only other way I could think of, yet the foil method is the proper way to handle this problem.

x and x will give you x^2

The sum of -1 and +2 is +1.

The product of -1 and +2 is -2.

Therefore, the trinomial is x^2+x-2.

[Or you can get the same thing by using FOIL.)

x^2+x-2=4

x^2+x-2-4=0

x^2+x-6=0

(x+3)(x-2)=0

x+3=0 or x-2=0

x=0-3 or x=0+2

x=-3 or x=2

x^2 -x + 2x - 2 = 4

x^2 + x - 6 = 0

(x -2)(x + 3) = 0

x = 2

x = -3

Proof

(2 - 1)(2 + 2) = 4

1(4) = 4

(-3 - 1)(-3 + 2) = 4

(-4)(-1) = 4