How do i solve quadratics and quadratic formula

Step-by-step explanation:

Multiply the first and last coefficient

Find a pair that has the product of ac (above) and the sum of b

Replace the b-term with the pair.

Divide the four terms into two-terms on the left side and two terms on the right side and factor out the common terms from each side.

This is reverse of the distributive property so the terms factored out (on the outside of the common term) combine to create a factor and the common term is the other factor.  

Set each factor equal to zero and solve for the variable.

1a. a = 1/2      a = -1

2a² + 3a + 1 = 0      → ac=2, b = 3    → use 1, 2  (product is 2 & sum is 3)

2a² + 2a + 1a + 1 = 0

2a² + 2a     +1a + 1        = 0

2a(a + 1)      +1(a + 1)      = 0

(2a + 1)(a + 1) = 0

2a + 1 = 0       and         a + 1 = 0

       a = 1/2    and               a = -1

1b. y = -5/2    y = -5

2y² + 5y - 25 = 0  → ac=-50, b = 5 → use 10, -5  (product is -50 & sum is -5)

2y² + 10y - 5y - 25 = 0

2y² + 10y      - 5y - 25        = 0

2y(y + 5)      -5(y + 5)      = 0

(2y - 5)(y + 5) = 0

2y + 5 = 0       and         y + 5 = 0

       y = -5/2    and               y = -5

1c. y = 5     y = 1/2

2y² - 11y + 5 = 0  → ac=10, b = -11 → use -1, -10  (product is 10 & sum is -11)

2y² - 1y - 10y + 5 = 0

2y² - 1y       -10y + 5        = 0

y(2y - 1)      -5(2y - 1)      = 0

(y - 5)(2y - 1) = 0

y - 5 = 0       and         2y - 1 = 0

     y = 5       and               y = 1/2

2? if not the correct answer you might need to provide more information

step-by-step explanation:

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".