A student is solving the problem x^2 + 10x+ ___ = 16 + ___ by the method of completing the square. What number should the student add to both sides?

Answer :

Answer:

I believe it could be any number because:

let y=any number

x^2+10x+y=16+y

x^2+10x+y-y=16+y-y

x^2+10x=16

you can add any number to both side and not change the solution.

The student should add 25 to both the sides of the quadratic equation x^2 + 10x+ ___ = 16 + ___

What is quadratic equation?

  • "It is an equation with degree two."
  • "The general form of quadratic equation is ax² + bx + c = 0"

What is the method of completing the square?

To complete the square for quadratic equation ax² + bx + c = 0 means we make the left hand side of the equation a perfect square.

1) First divide both the sides of the equation by the coefficient of x² that is 'a'

2) Add or subtract both the sides of the equation by (b/2)² that is complete the square

3) Solve the resulting equation to find the roots of the equation

For given example,

We have been given a quadratic equation x² + 10x+ ___ = 16 + ___

By comparing given equation with ax² + bx + c = 0,

we have a = 1, b = 10

To complete the square for given quadratic equation we add (b/2)² on both the sides.

⇒ (b/2)² = (10/2)²

⇒ (b/2)² = 5²

(b/2)² = 25

So, the quadratic equation would be,

⇒ x² + 10x + 25 = 16 + 25

⇒ (x + 5)² = 41

⇒ x + 5 = ±√41

⇒ x = -5 ± √41

So, the solutions of the quadratic equation would be x = -5 + √41 and x = -5 - √41

Therefore, the student should add 25 to both the sides of the quadratic equation x^2 + 10x+ ___ = 16 + ___

Learn more about the completing the square here:

https://brainly.com/question/4822356

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