Nonlinear Equations One Variable

Exponential equations on the SAT often become linear equations after rewriting both sides with the same base. When bases match, the exponents can be set equal.

Nonlinear equations in one variable include quadratic, radical, rational, absolute value, exponential, and polynomial equations. Solving often requires factoring, taking square roots, isolating a radical, using exponent rules, or checking for restrictions and extraneous solutions.

Nonlinear equations in one variable can include quadratics, equations with radicals, rational equations, powers, and equations written in factored or transformed forms. Useful strategies include factoring, applying the zero product property, using inverse operations, checking for extraneous solutions, and interpreting parameters from the structure of an equation.

Nonlinear equations in one variable can include quadratics, equations with radicals, rational equations, powers, and equations written in factored or transformed forms. Useful strategies include factoring, applying the zero product property, using inverse operations, checking for extraneous solutions, and interpreting parameters from the structure of an equation.

Nonlinear equations in one variable can include quadratics, equations with radicals, rational equations, powers, and equations written in factored or transformed forms. Useful strategies include factoring, applying the zero product property, using inverse operations, checking for extraneous solutions, and interpreting parameters from the structure of an equation.

Nonlinear equations in one variable can include quadratics, equations with radicals, rational equations, powers, and equations written in factored or transformed forms.

Parameter questions for nonlinear equations often use roots, discriminants, squared forms, radical equations, or factored forms.

Polynomial equations are often solved by moving all terms to one side, factoring, and applying the zero product property. Some SAT-style items ask for a particular solution, a nonzero solution, or the number of real solutions shown by factored form.

Quadratic equations may be solved by factoring, taking square roots, or using the discriminant to reason about the number of real solutions. SAT-style items often ask for one solution, a parameter, or the number of real solutions rather than both roots.

Radical and rational equations are common sources of errors because restrictions and extraneous solutions must be checked. Squaring and clearing denominators can introduce invalid candidates.

Radical and rational equations require attention to restrictions. Rational equations can have excluded denominator values, and radical equations can produce extraneous solutions after squaring.