Algebra questions plz help!?

Question

Solve

x^2-2x-15=0

x^2+12x=-36

x^2+3x-40=0

x^2-9x+18=0

explain plz so i can understand!

Answer 1

x^2-2x-15=0

(x-5)(x+3) = 0

Set x-5 = 0

So x = 5

And x+3 = 0

So x = -3

X = 5, -3

x^2+12x=-36

x^2 +12x +36 = 0

(x+6)(x+6) = 0

X = -6

x^2+3x-40=0

(x+8)(x-5) = 0

X = -8, 5

x^2-9x+18=0

(x-6)(x-3) = 0

X = 6, 3

Answer 2

There are many ways to solve quadratic equations.

I solved these ones by 'completing the square' . This method can only be used when the coefficient of x^2 is one (as all your equations are).

So by completing the square:

Lets look at these steps first and then we will apply them to your examples.

1. you must take the constant term over to the right

2. halve the coefficient of x and square it. you add this answer to both sides of the equation.

3. the left hand side is now the 'perfect square' but it needs to be put into a different form....

4. ... this is done by taking (x + half the coeffient of x)^2...

5. ...this equals the right hand side amount from step 3.

6. now we can solve and remember we will get two values for x.

This may sound confusing but hopefully you will understand what I am doing once I apply these steps to your examples.

Example one:

x^2 -2x =15 (taking constant over to right hand side)

halve coefficient of x gives    -1

square it gives   1

so add 1 to both sides and this gives:

x^2 -2x +1 = 15+1

now to find perfect square..

(x - 1)^2 = 16 (right hand side value)

(x minus one because -1 is half the coefficient of x)

now to solve:

(x - 1)^2 = 16

x - 1 = square root of 16

so... x = 1 (+ or -) the square root of 16

(plus OR minus because its square root. for example 2^2 = 4

and -2^2 also = 4)

so our two values of x are:

x = 1 - square root of 16

x= -3

AND

x = 1 + square root of 16

x = 5

So now lets try example 2:

x^2 + 12x = -36    (constant already on right hand side)

x^2 + 12x + (6)^2 = -36 + 6^2

x^2 + 12x + 36 = 0

(x + 6)^2 = 0

so only one value for x here...

x = -6

Example 3

x^2 + 3x -40 = 0

x^2 + 3x = 40

x^2 +3x + 2.25 = 40 + 2.25

(x + 1.5)^2 = 42.25

x = -1.5 +- square root of 42.25

so x = -1.5 - square root of 42.25

x = -8

And

x = -1.5 + square root of 42.25

x= 5

Example 4:

x^2 -9x +18 = 0

x^2 -9x +(-4.5)^2 = -18 + (-4.5)^2

x^2 -9x + 20.25 = 2.25

(x - 4.5)^2 = 2.25

x = 4.5 +- square root of 2.25

so x = 3 and x= 6

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Write it all out on paper so you can see it clearly.

I hope I have helped you with these questions!:-)

Sarah_Girl