Question

Rewrite the equation by completing the square.
4x² + 20r + 25 = 0
(x+...)^2=...

Answer 1

The equation
`4\cdot x^(2) + 20\cdot x + 25 = 0` is equal to
`\left(x + (5)/(2) \right)^(2) = 0`.

Explanation:

Let be the equation
`4\cdot x^(2) + 20\cdot x + 25 = 0`, we proceed to rewrite the equation solely by algebraic means:

1)
`4\cdot x^(2) + 20\cdot x + 25 = 0` Given

2)
`(2\cdot x)^(2) + 10\cdot (2\cdot x) + 25 = 0` Definition of power/Associative property

3)
`(2\cdot x + 5)^(2) = 0` Perfect square trinomial

4)
`2^(2)\cdot \left(x + (5)/(2) \right)^(2) = 0` Distributive property/
`(a\cdot b)^(c) = a^(c)\cdot b^(c)`

5)
`4\cdot (x + (5)/(2) )^(2) = 0` Definition of power

6)
`\left(x + (5)/(2) \right)^(2) = 0` Compatibility with multiplication/Commutative and modulative properties/
`a\cdot 0 = 0`