Basic Math Examples

$k^{2} + k - 4 = 2$

Step 1

Subtract $2$ from both sides of the equation.

$k^{2} + k - 4 - 2 = 0$

Step 2

Subtract $2$ from $- 4$ .

$k^{2} + k - 6 = 0$

Step 3

Factor $k^{2} + k - 6$ using the AC method.

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Step 3.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 6$ and whose sum is $1$ .

$- 2, 3$

Step 3.2

Write the factored form using these integers.

$(k - 2) (k + 3) = 0$

Step 4

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$k - 2 = 0$

$k + 3 = 0$

Step 5

Set $k - 2$ equal to $0$ and solve for $k$ .

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Step 5.1

Set $k - 2$ equal to $0$ .

$k - 2 = 0$

Step 5.2

Add $2$ to both sides of the equation.

$k = 2$

Step 6

Set $k + 3$ equal to $0$ and solve for $k$ .

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Step 6.1

Set $k + 3$ equal to $0$ .

$k + 3 = 0$

Step 6.2

Subtract $3$ from both sides of the equation.

$k = - 3$

Step 7

The final solution is all the values that make $(k - 2) (k + 3) = 0$ true.

$k = 2, - 3$