Solve: x² + 4x - 12 = 0
x = 2, x = -6
x = -2, x = -6
x = 3, x = -4
x = -3, x = 4

Solution:

Let us factorise the polynomial to find the value of x by splitting the middle term.

Step 1:

Identify the values of a, b and c.

In the above equation, a is coefficient of x² = 1, b is the coefficient of x = 4 and c is the constant term = - 12.

Step 2:

Multiply a and c and find the factors that add up to b.

1 × (- 12) = - 12

⇒ 6 and - 2 are the factors that add up to b.

Step 3:

Split bx into two terms.

x² + 6x - 2x - 12 = 0

Step 4:

Take out the common factors by grouping.

x(x + 6) - 2(x + 6) = 0

(x - 2) (x + 6) = 0

By putting the factors equal to zero we get two values of x

x - 2 = 0 and x + 6 = 0

x = 2 and x = -6

Thus, the two values that satisfy the equation are 2 and - 6.

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Solve: x² + 4x - 12 = 0

Summary:

The values of x for the equation x² + 4x - 12 = 0 is x = 2, -6 which satisfies the equation.