Content

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This article looks at a standard quadratic equation of the form:

ax + bx + c = 0

The article deduces a formula for the roots of a quadratic equation by complementing to a full square; numeric values ​​instead of a, b, c will not be substituted.

Steps

1. 1 Write an equation.
   
   ax + bx + c = 0
2. 2 Divide both sides of the equation by but.
   
   x + (b / a) x + c / a = 0
3. 3 Subtract s / a from both sides of the equation.
   
   x + (b / a) x = -c / a
4. 4 Divide the coefficient at NS (b / a) by 2, and then square the result. Add the result to both sides of the equation.
   
   (b / 2a)
   
   b / 4a
   
   x + (b / a) x + b / 4a = -c / a + b / 4a
5. 5 Simplify the expression by factoring the left side and adding the terms on the right side (find a common denominator first).
   
   (x + b / 2a) (x + b / 2a) = (-4ac / 4a) + (b / 4a)
   
   (x + b / 2a) = (b - 4ac) / 4a
6. 6 Take the square root of each side of the equation.
   
   √ ((x + b / 2a)) = ± √ ((b - 4ac) / 4a)
   
   x + b / 2a = ± √ (b - 4ac) / 2a
7. 7 Subtract b / 2a from both sides and you get the quadratic formula.
   
   x = (-b ± √ (b - 4ac)) / 2a

Tips

• Note: This method is also called full square's complement.

What do you need

• Pencil and paper