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The expression under the square root, $b^2 - 4ac$, is evaluated to determine the value added to or subtracted from $-b$ in the numerator. Its square root directly influences the final numerical values of the two solutions.

Conditions: The quadratic formula is being applied.; The coefficients $a$, $b$, and $c$ are known.

The expression under the square root, $b^2 - 4ac$, is evaluated to determine the value added to or subtracted from $-b$ in the numerator. Its square root directly influences the final numerical values of the two solutions.

Conditions: The quadratic formula is being applied.; The coefficients $a$, $b$, and $c$ are known.

When the quadratic formula yields an expression with a $\pm$ symbol, you must split it into two separate calculations. One calculation uses the plus sign, and the other uses the minus sign, to find both roots of the quadratic equation.

Conditions: The expression contains a $\pm$ symbol representing two possible values.; You are solving a quadratic equation.

When the quadratic formula yields an expression with a $\pm$ symbol, you must split it into two separate calculations. One calculation uses the plus sign, and the other uses the minus sign, to find both roots of the quadratic equation.

Conditions: The expression contains a $\pm$ symbol representing two possible values.; You are solving a quadratic equation.