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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Solving Nonlinear Equations by Substitution

Example

Solve for x: Solution = 18 Step 1 Write the equation in quadratic form. Subtract 18 from both sides. = 0 Step 2 Use an appropriate â€œuâ€ substitution.Substitute u for u2 + 3u - 18 = 0 Step 3 Solve the resulting equation. Factor the new equation. Use the Zero Product Property. Solve each equation for u. (u + 6)(u - 3) u + 6 = 0 or u - 3 u = -6 or u = 0 = 0 = 3 Step 4 Substitute the original expression for u. = 3 Step 5 Solve for the original variable. Multiply both sides of each equation by x. Write each equation in standard form. x2 + 4 = -6x or x2 + 4 x2 + 6x + 4 = 0 or x2 - 3x + 4 = 3x = 0

Neither equation factors. So, we will use the quadratic formula to solve each: So, there are four solutions:  The equation written in standard form is The graph of the corresponding function, is shown. The graph crosses the x-axis at the two locations corresponding to the two real solutions of the equation: Note that x is in a denominator and so it cannot equal 0. Therefore, the line x = 0 is a vertical asymptote.