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

Rewrite the equation by completing the square. 4x²

DESI111609

06.07.2021

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/ $a\cdot 0 = 0$

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