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 x² = 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

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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.