MATHICK! - Interactive Math Learning

How to solve:
Solve for x: x² + 5x + 6 = 0

(x + a)(x + b) = x² + (a + b)x + ab. Your goal is to find two numbers, a and b,

so that a + b = 5 and ab = 6.

List pairs of numbers that multiply together to get 6: 1 * 6 = 6, 2 * 3 = 6, -1 * -6 = 6, -2 * -3 = 6

From the pairs above, find the pair that adds up to 5: 2 + 3 = 5

These two numbers (2 & 3) are used to determine the factors. (x + 2) (x + 3) = 0.

Set each factor equal to 0: x + 2 = 0 , x + 3 = 0

Solve each equation: x = -2, x = -3

Another example: x² + 2x - 15 = 0

(x + a)(x + b) = x² + (a + b)x + ab. Your goal is to find a and b,

given that a + b = 2 and ab = -15.

List pairs of numbers that multiply together to get -15: 1 * -15 = -15, -1 * 15 = -15, -3 * 5 = -15, 3 * -5 = -15

From the pairs above, find the pair that adds up to 2: -3 + 5 = 2

These two numbers (-3 & 5) are used in the factors. (x - 3) (x + 5) = 0.

Set each factor equal to 0: x - 3 = 0 , x + 5 = 0

Solve each equation: x = 3, x = -5

Here's one to try:


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List pairs of numbers that multiply together to get 6:	`1 * 6 = 6, 2 * 3 = 6, -1 * -6 = 6, -2 * -3 = 6`
From the pairs above, find the pair that adds up to 5:	`2 + 3 = 5`
These two numbers (2 & 3) are used to determine the factors.	`(x + 2) (x + 3) = 0.`
Set each factor equal to 0:	`x + 2 = 0 , x + 3 = 0`
Solve each equation:	`x = -2, x = -3`

List pairs of numbers that multiply together to get -15:	`1 * -15 = -15, -1 * 15 = -15, -3 * 5 = -15, 3 * -5 = -15`
From the pairs above, find the pair that adds up to 2:	`-3 + 5 = 2`
These two numbers (-3 & 5) are used in the factors.	`(x - 3) (x + 5) = 0.`
Set each factor equal to 0:	`x - 3 = 0 , x + 5 = 0`
Solve each equation:	`x = 3, x = -5`