COMPARE AND CONTRAST SOLVING PROCESSES FOR LINEAR AND QUADRATIC EQUATIONS

SOLVING LINEAR EQUATIONS IN ONE VARIABLE

SOLVING QUADRATIC EQUATIONS

A linear equation has no exponent on its variable.

A quadratic equation can be written in the form
ax² + bx + c = 0 and a ¹ 0.

Simplify each side of the equation.

    * Distribute to clear parentheses.

    * Multiply by LCD to clear fractions.

    * Combine like terms.

Set the equation equal to zero.

Rewrite the equation so that the variable occurs on only 1 side

* Choose the variable term you want to eliminate

* Add its opposite to both sides of the equation

* Combine like terms.

Factor the polynomial side of the equation…

* This should not be factored until AFTER the equation has been set equal to zero.

Rewrite the equation so that there is no constant term on the variable side

*Add the opposite of the constant to both sides of the equation

*Combine like terms.

Set each factor equal to zero.

Divide both sides of the equation by the coefficient of the variable

Solve the resulting linear equations as instructed on in the left column of this page.

The final equation should be in the form
variable = constant

This is called the solution.

Check the solution

* Substitute the solution into the original equation

* Simplify each side using order of operations

* If this equation is true, your solution is correct