Solving Quadratic Equations
Solve the quadratic equation 16x2+16=−32x\displaystyle {16}{x}^{{2}}+{16}=-{32}{x} by using the Quadratic Formula. Verify your result by graphing and using the Intersection method.
    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 and in Approximate Form (Rounded to three decimal places as needed). Note that in some cases, the Exact Form and the Approximate Form may be the same.
  6. Note: If only one solution exists, x2\displaystyle {x}_{{2}} will equal DNE\displaystyle {D}{N}{E}
16x2+16=−32x\displaystyle {16}{x}^{{2}}+{16}=-{32}{x}
Exact Form
x1\displaystyle {x}_{{1}} =
 

Approximate Form
x1\displaystyle {x}_{{1}} =
  		Exact Form
x2\displaystyle {x}_{{2}} =
 

Approximate Form
x2\displaystyle {x}_{{2}} =
 

License