Question

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

Answer 1

Answer:

The equation $4\cdot x^{2} + 20\cdot x + 25 = 0$ is equal to $\left(x + \frac{5}{2} \right)^{2} = 0$.

Step-by-step 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) $2^{2}\cdot \left(x + \frac{5}{2} \right)^{2} = 0$ Distributive property/$(a\cdot b)^{c} = a^{c}\cdot b^{c}$

5) $4\cdot (x + \frac{5}{2} )^{2} = 0$ Definition of power

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