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Quadratic Equation Formula
The Quadratic Equation Formula is:
X = —––––––––––––
- b ± √(b2 - 4ac)
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.