Quadratic Equation Formula
The Quadratic Equation Formula is:
− b ± √(b2 − 4ac)
X = —––––––––––––
2a
A quadratic can be solved for x when the values for a, b and c of the Standard Equation, ax2 + bx + c, are known. The Quadratic Formula is factored from the Standard Equation by Completing the Square.
Place constant of Standard Equation to the right side of equals sign.
ax2 + bx = −c
Divide both sides of equation by a.
b −c
x2 + — x = —
a a
Complete the trinomial square.
b
x2 + — x
a
+
(
b
—
2a
)
2
=
−c
—
a
+
(
b
—
2a
)
2
Simplify equation terms step 1.
(
b
x + —–
2a
)
2
=
−c
—
a
×
4a — 4a
+
b2 —– 4a2
Simplify equation terms step 2.
(
b
x + —–
2a
)
2
=
b2 − 4ac
—––––
4a2
Square root both sides of equation.
(
b
x + —–
2a
)
=
√
b2 − 4ac
—––––
4a2
Simplify equation terms.
b
x + —–
2a
=
±
√(b2 − 4ac )
—––––––
√(4a2 )
Simplify equation terms.
b
x + —–
2a
=
±
√(b2 − 4ac )
—––––––
2a
Solve for x.
X =
− b ± √(b2 − 4ac )
____________
2a
= The Quadratic Equation Formula.
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