Examples

(6, 4)

$(6, 4)$

Step 1

x = 6

$x = 6$ and

x = 4

$x = 4$ are the two real distinct solutions for the quadratic equation, which means that

x - 6

$x - 6$ and

x - 4

$x - 4$ are the factors of the quadratic equation.

(x - 6) (x - 4) = 0

$(x - 6) (x - 4) = 0$

Step 2

Expand

(x - 6) (x - 4)

$(x - 6) (x - 4)$ using the FOIL Method.

Tap for more steps...

Step 2.1

Apply the distributive property.

x (x - 4) - 6 (x - 4) = 0

$x (x - 4) - 6 (x - 4) = 0$

Step 2.2

Apply the distributive property.

x \cdot x + x \cdot - 4 - 6 (x - 4) = 0

$x \cdot x + x \cdot - 4 - 6 (x - 4) = 0$

Step 2.3

Apply the distributive property.

x \cdot x + x \cdot - 4 - 6 x - 6 \cdot - 4 = 0

$x \cdot x + x \cdot - 4 - 6 x - 6 \cdot - 4 = 0$

x \cdot x + x \cdot - 4 - 6 x - 6 \cdot - 4 = 0

$x \cdot x + x \cdot - 4 - 6 x - 6 \cdot - 4 = 0$

Step 3

Simplify and combine like terms.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

Multiply

x

$x$ by

x

$x$ .

x^{2} + x \cdot - 4 - 6 x - 6 \cdot - 4 = 0

$x^{2} + x \cdot - 4 - 6 x - 6 \cdot - 4 = 0$

Step 3.1.2

Move

- 4

$- 4$ to the left of

x

$x$ .

x^{2} - 4 \cdot x - 6 x - 6 \cdot - 4 = 0

$x^{2} - 4 \cdot x - 6 x - 6 \cdot - 4 = 0$

Step 3.1.3

Multiply

- 6

$- 6$ by

- 4

$- 4$ .

x^{2} - 4 x - 6 x + 24 = 0

$x^{2} - 4 x - 6 x + 24 = 0$

x^{2} - 4 x - 6 x + 24 = 0

$x^{2} - 4 x - 6 x + 24 = 0$

Step 3.2

Subtract

6 x

$6 x$ from

- 4 x

$- 4 x$ .

x^{2} - 10 x + 24 = 0

$x^{2} - 10 x + 24 = 0$

x^{2} - 10 x + 24 = 0

$x^{2} - 10 x + 24 = 0$

Step 4

The standard quadratic equation using the given set of solutions

{6, 4}

${6, 4}$ is

y = x^{2} - 10 x + 24

$y = x^{2} - 10 x + 24$ .

y = x^{2} - 10 x + 24

$y = x^{2} - 10 x + 24$

Step 5

Enter YOUR Problem