Question

Can somebody help me with all three problems please

Answer 1

1. $x^{2} -10x +25 = 0$

These two numbers are: -5 and -5

-5 + (-5) = -10

-5 * -5 = 25

so...

(x - 5)(x - 5)

To find the roots set the factored numbers equal to zero and solve for x:

x - 5 = 0

x = 5

2. $x^{2} + 9x = -14$

This equation needs to be equal to zero, so bring -14 to the other side by adding 14 to both sides

$x^{2}+9x+14 =0$

Find two numbers that the sum is equal to 9 AND the multiplication of the numbers is 14

These numbers are 7 and 2

7 + 2 = 9

7*2 = 14

so...

(x + 2) (x + 7)

To find the roots set the each of the factored numbers equal to zero and solve for x:

x + 2 = 0

x = -2

x + 7 = 0

x = -7

3. $3x^{2} = 6x$

This equation needs to be equal to zero, so bring 6x to the other side by subtracting 6x to both sides

$3x^{2} -6x = 0$

In this equation you can factor out a 3 and an x:

3x (x - 2)

To find the roots set the each of the factored numbers equal to zero and solve for x:

3x = 0

3x/3 = 0/3

x = 0

x - 2 = 0

x = 2

Hope this helped!