DERIVING THE QUADRATIC FORMULA

ax² + bx + c = 0

Subtract c from both sides of the equation.

ax² + bx = -c

Divide both sides by the coefficient of x².

x² + (b/a)x = -c/a

Divide the coefficient of x by 2, square it, then add to both sides.
Note: This makes a perfect square on the left side.

x² + (b/a)x + b²/4a² = -c/a + b²/4a²

Simplify the left side into a square.

(x + b/2a)² = -c/a + b²/4a²

Simplify the right side by finding the lowest common denominator.

(x + b/2a)² = -4ac/4a² + b²/4a²

Add the fractions on the right.

(x + b/2a)² = (b² - 4ac)/4a²

Take the square root of both sides.
Note: The term +/-sqrt = plus or minus the square root of.

x + b/2a = +/-sqrt(b² - 4ac)/2a

Subtract b/2a from both sides and simplify.

x = [-b +/-sqrt(b² - 4ac)]/2a

Do you understand my child?

AN EXAMPLE USING THE QUADRATIC FORMULA

If...

2x² + 3x + 22 = 49

Then...

2x² + 3x + (-27) = 0

Using the quadratic formula...

x = [-3 +/-sqrt(3² - 4(2)(-27))]/[2(2)]

x = [-3 +/-sqrt(225)]/4

x = -3/4 +/-(15/4)

Therefore...

x = 3 or x = -4.5

PRINTER FRIENDLY

This tutorial created and designed by
Curtis Lee Hall

www.InTheBeginning.com

This webpage is dedicated to
Jodi
The Great Mathematician of Bates Hollow.
Truly a very precious spirit, a brilliant and beautiful soul.
(1Peter 3:4)

Intriguing - (adjective) causing a desire to know more; mysterious.

There is a River
by Mike De Lorenzo
My Father's House Ministries
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