1. Divide each term by the coefficient of the $x^2$ term.
- General form: $ax^2 + bx + c = 0$
- Divide by $a$: $x^2 + \frac{b}{a}x + \frac{c}{a} = 0$
- Example: $2x^2 + 7x - 15 = 0$
- Divide by $2$: $x^2 + \frac{7}{2}x - \frac{15}{2} = 0$
2. Add $-\frac{c}{a}$, the opposite of the constant term, to each side of the equation.
- General form: $x^2 + \frac{b}{a}x = -\frac{c}{a}$
- Example: $x^2 + \frac{7}{2}x = \frac{15}{2}$
3. Add $\left(\frac{b}{2a}\right)^2$, the square of $\frac{1}{2}$ of the coefficient of the $x$ term, to each side of the equation.
- General form: $x^2 + \frac{b}{a}x + \frac{b^2}{4a^2} = -\frac{c}{a} + \frac{b^2}{4a^2}$
- Example: $x^2 + \frac{7}{2}x + \left(\frac{7}{4}\right)^2 = \frac{15}{2} + \left(\frac{7}{4}\right)^2$
4. Factor the left side as the square of a binomial, and add the two terms on the right side after finding a common denominator.
- General form: $\left(x + \frac{b}{2a}\right)^2 = \frac{b^2 - 4ac}{4a^2}$
- Example: $\left(x + \frac{7}{4}\right)^2 = \frac{169}{16}$
5. Take the square root of both sides of the equation.
- General form: $x + \frac{b}{2a} = \pm \frac{\sqrt{b^2 - 4ac}}{2a}$
- Example: $x + \frac{7}{4} = \pm \frac{13}{4}$
6. Solve for $x$ by adding the opposite of the constant to each side.
- General form: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
- Example: $x = \frac{3}{2}$ or $-5$
Parent Tip: Review the logic above to help your child master the concept of pre calc worksheet.
