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Solving Quadratic Equations with Complex Solutions
Solve the quadratic equation by using the Quadratic Formula.
    Steps
  1. Write the equation in Standard Form
  2. Identify the coefficients a,b\displaystyle {a},{b} and c\displaystyle {c}.
  3. Substitute the values into the quadratic equation

    x=−b±b2−4ac2a\displaystyle {x}=\frac{{-{b}\pm\sqrt{{{b}^{{2}}-{4}{a}{c}}}}}{{{2}{a}}}

  4. Solve the equation for x1\displaystyle {x}_{{1}} and x2\displaystyle {x}_{{2}}

    x1=−b−b2−4ac2a\displaystyle {x}_{{1}}=\frac{{-{b}-\sqrt{{{b}^{{2}}-{4}{a}{c}}}}}{{{2}{a}}}      x2=−b+b2−4ac2a\displaystyle {x}_{{2}}=\frac{{-{b}+\sqrt{{{b}^{{2}}-{4}{a}{c}}}}}{{{2}{a}}}

  5. Write your answers in Exact Form.
  6. Note: If only one solution exists, x2\displaystyle {x}_{{2}} will equal DNE\displaystyle {D}{N}{E}
Exact Form
x1\displaystyle {x}_{{1}} =
Exact Form
x2\displaystyle {x}_{{2}} =

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