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If using the method of completing the square to solve the quadratic equation x^2-6x+32=0x 2 −6x+32=0, which number would have to be added to "complete the square"?

Respuesta :

Answer:

9.

Step-by-step explanation:

x^2-6x+32=0

You would have to add (-6/2)^24= 3^2 = 9.

x^2 - 6x + 9 = -32 + 9

(x - 3)^2 = -23

For quadratic equation [tex]x^2-6x+32=0[/tex], to complete the square we have to add 9

What is quadratic equation?

"An equation of the form [tex]ax^{2} +bx+c=0[/tex] where a, b, c are real numbers and a ≠ 0"

What is completing the square method?

  • "It is a method used to solve a quadratic equation by changing the form of the equation so that the left side is a perfect square."
  • For a quadratic equation [tex]ax^{2} +bx+c=0[/tex] ,                                            to complete the square, we need to add the term [tex](\frac{b}{2a} )^2[/tex] to both sides of the equation.

For given question,

We have been given an quadratic equation [tex]x^2-6x+32=0[/tex]

By comparing above quadratic equation with [tex]ax^{2} +bx+c=0[/tex] we have,

[tex]a=1,b=-6,c=32[/tex]

To solve the given quadratic equation by completing the square method, we need to add [tex](\frac{b}{2a} )^2[/tex]

[tex](\frac{b}{2a} )^2\\\\=(\frac{-6}{2\times 1} )^2\\\\=(-3)^2\\\\=9[/tex]

Therefore, for quadratic equation [tex]x^2-6x+32=0[/tex], to complete the square we have to add 9

Learn more about the completing the square method here:

https://brainly.com/question/4822356

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