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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 + ___
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:
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