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Section P7 Equations

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Solving Linear Equations in One Variable

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Example

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Linear Equations with Fractions

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Solving with Fractions

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Example

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Rational Equations

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Solving Rational Equations

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Example

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Solving a Formula for One of Its Variables

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Example

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Equations Involving Absolute Value

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Example

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Quadratic Equations and Factoring

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Example

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Quadratic Equations and the Square Root Property

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Example

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Quadratic Equations and Completing the Square

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StartAddResultFactored Form Obtaining a Perfect Square Trinomial

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Completing the Square

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Example

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Quadratic Equations and the Quadratic Formula

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Example

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Quadratic Equations and the Discriminant

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Example

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Graphing Calculator The real solutions of a quadratic equation ax 2 +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.

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Solving Polynomial Equations using the Graphing Calculator Repeat this process for each x intercept. By pressing 2 nd 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.

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Determining Which Method to Use

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Example

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Radical Equations

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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.

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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.

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Example Solve and check your answers:

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

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

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