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# what are the steps to solve this ax2 + bx + c = 0"

how do we solve it

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Michael F. | Mathematics TutorMathematics Tutor
4.7 4.7 (7 lesson ratings) (7)
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This answer comes from Littlewood's A University Algebra
ax2+bx+c=0  Multiply by 4a to get
4a2x2+4abx+4ac=0 Compete the square as
(2ax+b)2=4a2x2+4abx+b2 so that

4a2x2+4abx+4ac=(2ax+b)2-b2+4ac=0
(2ax+b)2=b2-4ac
2ax+b=±√(b2-4ac)
2ax=-b±√(b2-4ac)
x=(-b±√(b2-4ac))/(2a)
Jason S. | My goal is the success of my students. Knowledge-Patience-HonestyMy goal is the success of my students. K...
4.9 4.9 (115 lesson ratings) (115)
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Quadratic equation is derived by completing the square:

ax^2 + bx + c = 0

Subtract c from both sides:
ax^2 + bx = -c

Divide by a:
x^2 + (b/a)x = -c/a

Complete the square by taking half of b/a  and squaring it, then adding to both sides:
Note: (b/a) * 1/2 = b/(2a)
x^2 + (b/a)x + (b/(2a))^2 = -c/a + (b/(2a))^2

Simplify:

x^2 + (b/a)x + b^2/(4a^2) = -c/a + b^2/(4a^2)

Factor:
(x - (b/(2a))))^2 = -c/a + b^2/(4a^2)

Take the square root:

x + (b/(2a)) = +/-  sqrt(-c/a + b^2/(4a^2))

Subtract b/(2a) from both sides:

x = -b/(2a) +/- sqrt(-c/a + b^2/(4a^2))

Simplify:

x = -b/(2a) +/- sqrt(  -4ac             b^2          )
-------  +   ---------
4a^2           4a^2

x = -b +/- sqrt (b^2 - 4ac)
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2a