# 14.3 Equations in Quadratic Form

**Substituting to Fit Quadratic Form • Solving Equations in Quadratic Form • Extraneous Roots**

Often, we encounter equations that can be solved by methods applicable to quadratic equations, even though these equations are not actually quadratic.

# NOTE

[They do have the property, however, that with a proper substitution they may be written in the form of a quadratic equation.]

All that is necessary is that the equation have terms including some variable quantity, its square, and perhaps a constant term. The following example illustrates these types of equations.

# EXAMPLE 1 Identifying quadratic form

The equation $x\hspace{0.17em}-\hspace{0.17em}2\sqrt{x}\hspace{0.17em}-\hspace{0.17em}5\hspace{0.17em}=\hspace{0.17em}0$ is an equation in quadratic form, because if we let $y\hspace{0.17em}=\hspace{0.17em}\sqrt{x}\hspace{0.17em},\hspace{0.17em}$ we have $x\hspace{0.17em}=\hspace{0.17em}{(\sqrt{x})}^{2}\hspace{0.17em}=\hspace{0.17em}{y}^{2}$

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