Prove the quadratic formula

ax² + bx + c = 0

x = (-b ± √(b² - 4ac))/2a

First, rewrite the first equation so that the first coefficient is 1. Divide everything by a.

(ax² + bx + c = 0)/a =

x² + (b/a)x + (c/a) = 0

Isolate (c/a) by subtracting (c/a) from both sides

x² + (b/a)x + (c/a) (-(c/a) = 0 (- (c/a)

x² + (b/a)x = 0 - (c/a)

Add spaces

x² + (b/a)x          =  -c/a

Take 1/2 of the middle term's coefficient and square it. Remember that what you add to one side, you add to the other.

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

Simplify the left side of the equation.

x² + (b/a)x + (b/2a)² = (x + (b/2a))²

(x + b/2a))² = ((b²/4a²) - (4ac/4a²)) -> ((b² - 4ac)/(4a²))

Take the square root of both sides of the equation

√(x + b/2a))² = √((b²/4a²) - (4ac/4a²))

x + b/(2a) = (±√(b² - 4ac)/2a

Simplify. Isolate the x.

x = -(b/2a) ± (∛b² - 4ac)/2a = (-b ± √(b² - 4ac))/2a

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step-by-step explanation:

ok one would be money, and the other would be refreshments or something similar. if each bag of popcorn is 5.00 and each drink is half of that that means drinks are 2.50 the proper way to do that would to look and see how much of each you can buy without exceeding a limit of 30.00

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step-by-step explanation: