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:

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40 minutes

step-by-step explanation:

add the time and multiply by 2