02Gnonlinear

= Solving Non-Linear Equations = toc

Even when the equation is not linear, the idea of how to solve it remains the same:
 * Undo the things that have been done to the variable
 * Do the same things to both sides of the equation

Non-linear equations will sometimes have more than one solution. A correct answer shows __all__ the possible solutions.

** Example **
math \textbf{(a)} \quad \text{Solve : } \sqrt{x} = 0.8 math

{to undo the square root, we will square both sides}

math \\ . \qquad \quad \;\;\; \sqrt{x} = 0.8 \\ \\ . \qquad \Big( \sqrt{x} \Big)^2 = \Big( 0.8 \Big)^2 \\ \\ . \qquad \qquad \; x = 0.16 math

math \textbf{(b)} \quad \text{Solve : } x^2 = 100 math

{to undo the square, we will take the square root of both sides}

math \\ . \qquad x^2 = 100 \\ \\ . \qquad x = \pm \sqrt{100} \\ \\ . \qquad x = \pm 10 math

The ± symbol means "//plus and minus//"

{x = ±10 means there are two solutions : } math x = +10 \quad \textit{and} \quad x = -10 math

{__both__ answers are solutions to x 2 = 100}

math \textbf{(c)} \quad \text{Solve : } 2x^2 - 5 = 1 math

math \\ . \qquad 2x^2-5 = 1 \qquad \textit{add 5} \\ \\ . \qquad \qquad 2x^2=6 \qquad \textit{divide by 2} \\ \\ . \qquad \qquad \;\; x^2 = 3 \qquad \textit{take square root} \\ \\ . \qquad \qquad \;\; x = \pm \sqrt{3} \qquad \textbf{Exact Answer} \\ \\ . \qquad \qquad \;\; x = \pm 1.732 \qquad \textbf{Approx. Answer} math

This topic continues in Chapter 5: Quadratic Equations

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