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Answer:
The equation [tex]4\cdot x^{2} + 20\cdot x + 25 = 0[/tex] is equal to [tex]\left(x + \frac{5}{2} \right)^{2} = 0[/tex].
Step-by-step explanation:
Let be the equation [tex]4\cdot x^{2} + 20\cdot x + 25 = 0[/tex], we proceed to rewrite the equation solely by algebraic means:
1) [tex]4\cdot x^{2} + 20\cdot x + 25 = 0[/tex] Given
2) [tex](2\cdot x)^{2} + 10\cdot (2\cdot x) + 25 = 0[/tex] Definition of power/Associative property
3) [tex](2\cdot x + 5)^{2} = 0[/tex] Perfect square trinomial
4) [tex]2^{2}\cdot \left(x + \frac{5}{2} \right)^{2} = 0[/tex] Distributive property/[tex](a\cdot b)^{c} = a^{c}\cdot b^{c}[/tex]
5) [tex]4\cdot (x + \frac{5}{2} )^{2} = 0[/tex] Definition of power
6) [tex]\left(x + \frac{5}{2} \right)^{2} = 0[/tex] Compatibility with multiplication/Commutative and modulative properties/[tex]a\cdot 0 = 0[/tex]