Answer:
(x+3)² = 64
Explanation:
(x+a)² = b
so, let's see the details of the square calculation :
x² + 2ax + a² = b
so, now we have in our problem the specific equation
x² +3x - 69 = -3x - 14
now, let's group and combine all expressions of x
x² + 6x - 69 = -14
compare to the general square equation.
x² is in both expressions. nothing else needs to be done for that part.
2ax must be equal to 6x.
=> 2a = 6
a = 3
so, our general swathe square equation turns then into
(x+3)² = b. or
x² + 6x + 3² = b
x² + 6x + 9 = b
now bring this again into our specific equation and see how we have to transform the remaining numbers to keep the equation true, and to show us b :
x² + 6x + 9 - 78 = -14 (because 9-78 is again -69)
x² + 6x + 9 = 64
=> b = 64
so, the form (x+a)²=b for our specific equation is
(x+3)² = 64