# Solve for x in the equation x² + 20x + 100 = 36.

x = - 16 or x = - 4, x = - 10, x = - 8, x = 4 or x = 16

**Solution:**

**Step 1: **Simplify the given quadratic equation in the standard form ax² + bx + c = 0

x² + 20x + 100 = 36 can be written as x² + 20x + 64 = 0.

**Step 2: **Identify the values of a, b and c.

In the above equation, a is coefficient of x^{2} = 1,

b is the coefficient of x = 20 and

c is the constant term = 64.

**Step 3: **Let us factorize the quadratic equation to find the value of x by splitting the middle term.

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

1 × (64) = 64

⇒ 16 and 4 are the factors of 64 that add up to b.

**Step 4: **Split bx into two terms.

x² + 16x + 4x + 64 = 0

**Step 5: **Take out the common factors by grouping.

x(x + 16) + 4(x +16) = 0

(x + 4) (x + 16) = 0

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

x + 4 = 0 and x + 16 = 0

x = - 4 and x = - 16

Thus the values of x in the given equation x² + 20x + 100 = 36 are x = - 4 and x = - 16

## Solve for x in the equation x² + 20x + 100 = 36.

x = - 16 or x = - 4, x = - 10, x = - 8, x = 4 or x = 16

**Summary:**

The factors of the equation x² + 20x + 100 = 36 are x = - 4 or x = -16.