Solve the given quadratic equation 100x² - 20x + 1 = 0 by factorization?

Finding the Factors

We need to find two numbers that multiply to 100 and add to -20. The numbers that fit this requirement are -10 and -10 since:

• -10 × -10 = 100
• -10 + -10 = -20

Rewriting the Equation

Now, we can rewrite the middle term of the equation using these factors:

100x² - 10x - 10x + 1 = 0

Grouping Terms

Next, we group the terms:

(100x² - 10x) + (-10x + 1) = 0

Factoring by Grouping

Now, we factor out the common terms from each group:

• From the first group: 10x(10x - 1)
• From the second group: -1(10x - 1)

So, we have:

10x(10x - 1) - 1(10x - 1) = 0

Final Factorization

This can be factored further as:

(10x - 1)(10x - 1) = 0

Solving for x

Setting each factor equal to zero gives:

• 10x - 1 = 0 → x = 1/10

Since both factors are the same, the solution is:

x = 0.1

Summary

The solution to the quadratic equation 100x² - 20x + 1 = 0 is x = 0.1.