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Solve by factoring x2 + 10x – 24 = 0

Solve by factoring x2 + 10x – 24 = 0

Answer

x = 2, -12

Explanation

x² + 10x – 24 = 0

Factorize x² + 10x -24 using the AC method

Consider the form x² + bx + c

Look for a pair of integers that the product is c and whose sum is b.

In this case whose product is -24 and whose sum is 10

6, 4; 6 x 4 = 24; 6 + 4 = 10

-2, 12; -2 x 12 = -24; -2 + 12 = 10

Write the factored form using these integers

(x – 2)(x + 12) = 0

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

x -2 = 0; x + 12 = 0

Set x – 2 equal to 0 and solve for x

x – 2 = 0

Add 2 to both sides of the equation.

x – 2 + 2 = 0 + 2

Set x + 12 equal to 0 and solve for x.

x + 12 = 0

Subtract 12 from both sides of the equation

x + 12 – 12 = 0 – 12

x= -12

Thus, 2, -12 makes (x – 2)(x + 12) = 0 true

Therefore, x=2, -12.

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