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Plus or Minus (±) — Definition, Formula & Examples

Plus or minus (±) is a mathematical symbol that represents two operations at once: addition and subtraction. When you see ±, it tells you there are two possible answers — one found by adding and one found by subtracting.

The symbol ± placed before a quantity indicates that the quantity may be either added to or subtracted from a given expression, yielding two distinct values. Formally, if a±ba \pm b appears, it represents the set {a+b, a−b}\{a + b,\, a - b\}.

Key Formula

x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
Where:
  • aa = Coefficient of x² in a quadratic equation
  • bb = Coefficient of x in a quadratic equation
  • cc = Constant term in a quadratic equation
  • ±\pm = Indicates two solutions: one using + and one using −

How It Works

Whenever you encounter ±, replace it with + to get one answer, then replace it with − to get a second answer. The most common place you will see ± is in the quadratic formula, where a square root can be positive or negative. It also appears in error ranges, such as a measurement of 50±250 \pm 2 cm, meaning the true value lies between 48 cm and 52 cm. Think of ± as a shorthand that saves you from writing two separate equations.

Worked Example

Problem: Solve x² − 9 = 0 using the ± symbol.
Step 1: Isolate x².
x2=9x^2 = 9
Step 2: Take the square root of both sides. Because squaring either a positive or negative number gives 9, use ±.
x=±9x = \pm\sqrt{9}
Step 3: Evaluate the two cases: x = +3 and x = −3.
x=+3orx=−3x = +3 \quad \text{or} \quad x = -3
Answer: x = 3 or x = −3

Another Example

Problem: A rope measures 120 ± 5 cm. What are the shortest and longest possible lengths?
Step 1: Use the + case to find the longest possible length.
120+5=125 cm120 + 5 = 125 \text{ cm}
Step 2: Use the − case to find the shortest possible length.
120−5=115 cm120 - 5 = 115 \text{ cm}
Answer: The rope could be as short as 115 cm or as long as 125 cm.

Why It Matters

You will use ± constantly in algebra courses when solving quadratic equations with the quadratic formula. In science classes, ± shows up in measurement uncertainty — for instance, reporting a temperature as 22±0.5°22 \pm 0.5°C. Understanding this symbol is essential for correctly identifying all solutions to an equation rather than accidentally dropping one.

Common Mistakes

Mistake: Only using the positive value and ignoring the negative one.
Correction: The ± symbol means there are two answers. Always evaluate both the + case and the − case, then check whether both solutions are valid in context.
Mistake: Thinking ± means approximately equal.
Correction: The symbol for approximately equal is ≈. The ± symbol specifically means "add or subtract," not "close to."

Related Terms