Question

ax2+bx+c=0 solution by completing the square a is not = 0​

Answer 1

Solution:

Given quadratic equation

ax²+bx+c=0

Divide each term by a , we get

=> x²+(b/a)x+c/a = 0

=> x²+(b/a)x = -c/a

=> x²+2*x*(b/2a) = -c/a

=> x²+2*x*(b/2a)+(b/2a)²=-c/a+(b/2a)²

=> (x+b/2a)² = -c/a + b²/4a²

=> (x+b/2a)² = (-4ac+b²)/4a²

=> x+b/2a =±√[(b²-4ac)/4a²]

=> x = -b/2a ± √(b²-4ac)/2a

=> x = [-b±√(b²-4ac)]/2a

Therefore,

x = [-b+√(b²-4ac)]/2a,

x = [-b+√(b²-4ac)]/2a, Or

x = [-b+√(b²-4ac)]/2a, Or x = [-b-√(b²-4ac)]/2a

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