Equations with Quadratic Expressions on Both Sides of the Equal Sign

9.1.1 Equations with Quadratic Expressions on Both Sides of the Equal Sign

9.1.1 • Equations with Quadratic Expressions on Both Sides of the Equal Sign

In each equation, what expression could be substituted for $a$ so the equation is true for all values of $x$ ?

$x^{2} = a^{2}$

Compare your answer:

$a = x$ .

$(3 x)^{2} = a^{2}$

Compare your answer:

$a = 3 x$ .

$a^{2} = 7 x \cdot 7 x$

Compare your answer:

$a = 7 x$ .

$25 x^{2} = a^{2}$

Compare your answer:

$a = 5 x$ .

$a^{2} = \frac{1}{4} x^{2}$

Compare your answer:

$a = \frac{1}{2} x$ .

$a^{2} = (x + 1)^{2}$

Compare your answer:

$a = x + 1$ .

$(2 x - 9) (2 x - 9) = a^{2}$

Compare your answer:

$a = 2 x - 9$ .