Solve x² - 7x + 12 = 0

x = -3, x = - 4
x = 3, x = 4
x = 2, x = 6
x = -2, x = -6

Solution:

Let us factorize the quadratic equation 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 = - 7 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

⇒ - 3 and - 4 are the factors that add up to b.

Step 3: Split bx into two terms.

x² - 3x - 4x + 12 = 0

Step 4: Take out the common factors by grouping.

x(x - 3) - 4 (x - 3) = 0

(x - 3) (x - 4) = 0

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

x - 3 = 0 and x - 4 = 0

x = 3 and x = 4

Thus, the two values that satisfy the equation are 3 and 4.

Solve x² - 7x + 12 = 0

Summary:

The values of x for the equation x² - 7x + 12 = 0 is x = 3, 4 which satisfies the equation.