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Which of the following is equivalent to 0 equals 3 x squared minus 12 x minus 15 when completing the square?

Sagot :

doomdabomb
Answer:

x = 5, -1

Step-by-step explanation:

0 = 3x^2 - 12x - 15 or

3x^2 - 12x - 15 = 0

By solving for x, use the Quadratic Formula.

… x = 5 and/or -1

After completing the square the quadratic equation [tex]3x^{2} -12x-15=0[/tex] is equivalent to [tex](x-2)^2=3^2[/tex].

What is a quadratic equation?

"It is a polynomial equation with degree two."

What is completing the square method?

"It is a method that is used for converting a quadratic expression of the form [tex]ax^2 + bx + c[/tex] to [tex]a(x - h)^2 + k[/tex] "

For given example,

We have been given a quadratic equation.

[tex]3x^{2} -12x-15=0[/tex]

First we divide above quadratic equation by 3,

[tex]x^{2} -4x-5=0\\\\x^2-4x=5[/tex]                             ................(i)

Now for completing the square first find [tex](\frac{-b}{2a} )[/tex]

[tex]\frac{-b}{2a}\\=\frac{-(-4)}{(2)(1)}\\\\ =\frac{4}{2}\\\\ =2[/tex]

Add [tex](\frac{-b}{2a} )^2[/tex] on both the sides of equation (i),

[tex]x^{2} -4x+4=5+4\\\\(x-2)^2=9\\\\(x-2)^2=3^2[/tex]

Therefore, after completing the square the quadratic equation [tex]3x^{2} -12x-15=0[/tex] is equivalent to [tex](x-2)^2=3^2[/tex].

Learn more about completing the square here:

https://brainly.com/question/4822356

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