Solve for a 2a^2-46a+252=0

$2 a^{2} - 46 a + 252 = 0$

Step 1

Factor the left side of the equation.

Factor $2$ out of $2 a^{2} - 46 a + 252$ .

Factor $2$ out of $2 a^{2}$ .

$2 (a^{2}) - 46 a + 252 = 0$

Factor $2$ out of $- 46 a$ .

$2 (a^{2}) + 2 (- 23 a) + 252 = 0$

Factor $2$ out of $252$ .

$2 a^{2} + 2 (- 23 a) + 2 \cdot 126 = 0$

Factor $2$ out of $2 a^{2} + 2 (- 23 a)$ .

$2 (a^{2} - 23 a) + 2 \cdot 126 = 0$

Factor $2$ out of $2 (a^{2} - 23 a) + 2 \cdot 126$ .

$2 (a^{2} - 23 a + 126) = 0$

Factor.

Factor $a^{2} - 23 a + 126$ using the AC method.

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 $126$ and whose sum is $- 23$ .

$- 14, - 9$

Write the factored form using these integers.

$2 ((a - 14) (a - 9)) = 0$

Remove unnecessary parentheses.

$2 (a - 14) (a - 9) = 0$

Step 2

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

$a - 14 = 0$

$a - 9 = 0$

Step 3

Set $a - 14$ equal to $0$ and solve for $a$ .

Set $a - 14$ equal to $0$ .

$a - 14 = 0$

Add $14$ to both sides of the equation.

$a = 14$

Step 4

Set $a - 9$ equal to $0$ and solve for $a$ .

Set $a - 9$ equal to $0$ .

$a - 9 = 0$

Add $9$ to both sides of the equation.

$a = 9$

Step 5

The final solution is all the values that make $2 (a - 14) (a - 9) = 0$ true.

$a = 14, 9$

Solve for a 2a^2-46a+252=0

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