Answer:
0=x²+12x−69 Subtract x² from both sides. −x²=12x−69 Subtract 12x from both sides. −x²−12x=−69 Divide both sides by -1. x²+12x=69 Add (12/2)^2=36 to both sides to complete the square.
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The required function completing the square is ( x + 6 )² = 105.
To rewrite the function by completing the square f(x) = x² + 12x - 69.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Function f(x) = x² + 12x - 69
In order to find the perfect square of the function.
f(x) = 0
x² + 12x - 69 = 0
Half the coefficient of x
coefficient of x = 12
=12/2= 6
Add and subtract the square of it in the equation
6² = 36
x² + 12x - 69 +36 -36 = 0
Rearrange,
x² + 12x +36 =69+36
x² + 6x + 6x +36 =105
x( x + 6 ) + 6 ( x + 6) =105
(x+6)(x+6) = 105
(x+6)² = 105
Thus, The required function completing the square is ( x + 6 )² = 105.
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