Section P7 Equations

Solving Linear Equations in One Variable

Example

Linear Equations with Fractions

Solving with Fractions

Example

Example

Rational Equations

Solving Rational Equations

Example

Example

Example

Solving a Formula for One of Its Variables

Example

Example

Equations Involving Absolute Value

Example

Example

Quadratic Equations and Factoring

Example

Example

Example

Quadratic Equations and the Square Root Property

Example

Example

Quadratic Equations and Completing the Square

Obtaining a Perfect Square Trinomial Start Add Result Factored Form

Completing the Square

Example

Example

Example

Quadratic Equations and the Quadratic Formula

Example

Example

Quadratic Equations and the Discriminant

Example

Graphing Calculator The real solutions of a quadratic equation ax2+bx+c=0 correspond to the x-intercepts of the graph. The U shaped graph shown below has two x intercepts. When y=0, the value(s) of x will be the solution to the equation. Since y=0 these are called the zeros of the function.

Solving Polynomial Equations using the Graphing Calculator By pressing 2nd Trace to get Calc, then the #2,you get the zeros. It will ask you for left and right bounds, and then a guess. For left and right bounds move the blinking cursor (using the arrow keys-cursor keys) to the left and press enter. Then move the cursor to the right of the x intercept and press enter. Press enter when asked to guess. Then you get the zeros or solution. Repeat this process for each x intercept.

Determining Which Method to Use

Example

Example

Example

Radical Equations

A radical equation is an equation in which the variable occurs in a square root, cube root, or any higher root. We solve the equation by squaring both sides.

This new equation has two solutions, -4 and 4 This new equation has two solutions, -4 and 4. By contrast, only 4 is a solution of the original equation, x=4. For this reason, when raising both sides of an equation to an even power, check proposed solutions in the original equation. Extra solutions may be introduced when you raise both sides of a radical equation to an even power. Such solutions, which are not solutions of the given equation are called extraneous solutions or extraneous roots.

Example Solve and check your answers:

(a) (b) (c) (d)

(a) (b) (c) (d)