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Answer:
x = [-b ±√(b² - 4ac)]/2a
Step-by-step explanation:
ax² + bx + c = 0
dividing through by a, we have
ax²/a + bx/a + c/a = 0
x² + bx/a + c/a = 0
x² + bx/a = -c/a
we now add th square of half the coefficient of x to both sides, thus
x² + bx/a + (b/2a)² = -c/a + (b/2a)²
simplifying the left hand side and right hand side, we have
(x + b/2a)² = -c/a + b²/4a²
re-arranging, we have
(x + b/2a)² = b²/4a² - c/a
taking L.C.M of the right hand side, we have
(x + b/2a)² = (b² - 4ac)/4a²
taking square-root of both sides, we have
√(x + b/2a)² = ±√[(b² - 4ac)/4a²]
x + b/2a = ±√(b² - 4ac)/2a
So, x = -b/2a ±√(b² - 4ac)/2a
taking the L.C.M of the right hand side, we have
x = [-b ±√(b² - 4ac)]/2a