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Describe how to derive the quadratic formula from a quadratic equation in standard form

User Hypno
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2 Answers

2 votes

Answer:

The quadratic formula is derived from a quadratic equation in standard form when solving for x by completing the square. The steps involve creating a perfect square trinomial, isolating the trinomial, and taking the square root of both sides. The variable is then isolated to give the solutions to the equation.

Explanation:

:)

User Tim Klein
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2 votes

Firstly we learn the standard quadratic equation,

ax²+bx+c=0

where a,b,c are real numbers.

Now solve the quadratic equation using the Complete the square method.

Rewriting part of the equation as a perfect square trinomial. If you complete the square on the generic equation ax² + bx + c = 0 and then solve for x,

ax²+bx=-c

x² +
(b)/(a) x=-c

add both the side
((b)/(2a) )^(2)

x² +
(b)/(a) x+
((b)/(2a))^(2) = -(c)/(a) + ((b)/(2a))^(2)


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

take square root both the side


x = \frac{-b+\sqrt{b^(2)-4ac}}{2a}


x= \frac{-b-\sqrt{b^(2)-4ac}}{2a}

User Peter Crabtree
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