What are the solutions of the quadratic equation 0 = 4(x - 3)² - 16?

Solution:

Given,

The quadratic equation 0 = 4(x - 3)² - 16.

Using binomial theorem, (a - b)² = a² - 2ab + b² to expand (x - 3)².

0 = 4(x² - 6x + 9 ) - 16.

Using distributive property to multiply 4 by x² - 6x + 9.

0 = 4x² - 24x + 36 - 16.

Subtract 16 from 36 to get 20.

0 = 4x² - 24x + 20.

4x² - 24x + 20 = 0.

Divide both sides by 4.

x² - 6x + 5 = 0.

To solve the equation, factor and rewrite as x² + ax + bx + 5

a + b = -6, ab = 1(5) = 5.

a = -5, b = -1.

Rewriting x² - 6x + 5 as

(x² - 5x) + (-x + 5)

Factor x in the first and -1 in the second group.

x(x - 5) - (x - 5)

Factor out common term

(x - 5)(x - 1)

By solving the above, we get

x = 5, x = 1

Therefore, x = 5, x = 1.

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What are the solutions of the quadratic equation 0 = 4(x - 3)² - 16?

Summary:

The solutions of the quadratic equation 0 = 4(x - 3)² - 16 is 5 , 1.