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Studentka2010 [4]
3 years ago
13

X^3-13x^2+40x=0 quadratic

Mathematics
1 answer:
lutik1710 [3]3 years ago
6 0

Answer:

x(x-5)(x-8)

or

x=5

x=8

Step-by-step explanation:

  1. x(x^2-13x+40)
  2. x(x-5) (x-8)
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marishachu [46]

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(a+b)^2=a^2+2ab+b^2\qquad(*)\\\\-------------------------------\\\\x^2+6x-16=0\qquad\text{add 16 to both sides}\\\\x^2+6x=16\\\\x^2+2(x)(3)=16\qquad\text{add}\ 3^2\ \text{to both sides}\\\\\underbrace{x^2+2(x)(3)+3^2}_{(*)}=16+3^2\\\\(x+3)^2=16+9\\\\(x+3)^2=25\Rightarrow x+3=\pm\sqrt{25}\\\\x+3=-5\ \vee\ x+3=5\qquad\text{subtract 3 from both sides}\\\\\boxed{x=-8\ \vee\ x=2}

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