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The expression you presented is not an equation.

Do you mean ax2 + bx = c?

Do you mean to solve it for x?

I'm assuming that's the case, but you need to be more clear on your question.

To solve for x then, the technique to use is called completing the square:

ax2 + bx = c

Multiply both sides by a:

a2x2 + abx = ac

Add the square of b/2 to both sides:

a2x2 + abx + (b/2)2 = ac + (b/2)2

We now have a perfect square on the left, simplify:

(ax + b/2)2 = ac + b2 / 4

(ax + b/2)2 = (4ac + b2) / 4

And now solve for x:

ax + b/2 = ±[(4ac + b2) / 4]1/2

ax + b/2 = ± √(4ac + b2) / 2

ax = [-b ± √(4ac + b2)] / 2

x = [-b ± √(4ac + b2)] / 2a

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13y ago

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