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By completing the square, find the solutions of x which satisfy the equation x^2+14x-1=0

When applying completing the square method, the main goal is to change the format of the equation from:

ax²+bx+c = 0 ⇒ a(x+d)² + e= 0

If we compare both the equations, in the second one we have the variables “d” and “e” instead of “b” and “c”.

Both “d’ and “e” can be calculated through the following formulas:

d= b/2a
e= c- b²/4a

So if we look at our quadratic equation, it is x² + 14x - 1= 0.

a= 1
b= 14
c= -1


d= 14/2(1)
  = 7

e= -1 - (14)²/4(1)
  = -1- 49
  = -50

If we plug these values into the completed square form, the equation equals to:

(x² + 7) - 50 = 0

However, if in a quadratic equation, the coefficient of x² is greater than 1, then you take the number common from the entire equation.

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