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To solve a quadratic equation using the quadratic formula, first rewrite the equation in standard form $ax^2 + bx + c = 0$ and identify the coefficients $a$, $b$, and $c$. Substitute these values into the formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

Conditions: The equation must be in standard quadratic form: $ax^2 + bx + c = 0$.; The leading coefficient $a$ must not be zero ($a \neq 0$).

To solve a quadratic equation using the quadratic formula, first rewrite the equation in standard form $ax^2 + bx + c = 0$ and identify the coefficients $a$, $b$, and $c$. Substitute these values into the formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

Conditions: The equation must be in standard quadratic form: $ax^2 + bx + c = 0$.; The leading coefficient $a$ must not be zero ($a \neq 0$).

To verify a calculated root, substitute the value of the root back into the original quadratic equation for the variable $x$. Follow the order of operations to simplify the expression.

Conditions: You have a candidate solution for $x$.; The original quadratic equation is available.

To verify a calculated root, substitute the value of the root back into the original quadratic equation for the variable $x$. Follow the order of operations to simplify the expression.

Conditions: You have a candidate solution for $x$.; The original quadratic equation is available.

To substitute coefficients into the quadratic formula, first identify $a$, $b$, and $c$ from the standard form $ax^2 + bx + c = 0$. Replace $a$, $b$, and $c$ in the formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ with their numerical values.

Conditions: The equation is in standard form $ax^2 + bx + c = 0$.; The coefficients $a$, $b$, and $c$ have been correctly identified.

To substitute coefficients into the quadratic formula, first identify $a$, $b$, and $c$ from the standard form $ax^2 + bx + c = 0$. Replace $a$, $b$, and $c$ in the formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ with their numerical values.

Conditions: The equation is in standard form $ax^2 + bx + c = 0$.; The coefficients $a$, $b$, and $c$ have been correctly identified.

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.

Yes, consider the equation $6x^2 - 17x + 12 = 0$. The coefficients are $a=6$, $b=-17$, and $c=12$.

Conditions: The quadratic equation has at least one negative coefficient.; The equation is in standard form $ax^2 + bx + c = 0$.

Yes, consider the equation $6x^2 - 17x + 12 = 0$. The coefficients are $a=6$, $b=-17$, and $c=12$.

Conditions: The quadratic equation has at least one negative coefficient.; The equation is in standard form $ax^2 + bx + c = 0$.