Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Dec 08, 2023

Solve $(x+6)(x-6)=0$ for $x$ , express answer in reduced fraction form.

STEP 1

Assumptions
1. We are given the equation $(x+6)(x-6)=0$ .
2. We need to find all values of $x$ that satisfy the equation.
3. The equation is a product of two factors set equal to zero.

STEP 2

Use the Zero Product Property, which states that if the product of two factors is zero, then at least one of the factors must be zero.
$(x+6)(x-6) = 0 \Rightarrow x+6 = 0 \text{ or } x-6 = 0$

STEP 3

Solve the first equation $x+6 = 0$ for $x$ .
$x+6 = 0 \Rightarrow x = -6$

STEP 4

Solve the second equation $x-6 = 0$ for $x$ .
$x-6 = 0 \Rightarrow x = 6$

STEP 5

Combine the solutions from STEP_3 and STEP_4 to provide the complete solution set.
$x = -6, 6$
The solutions to the equation $(x+6)(x-6)=0$ are $x = -6$ and $x = 6$ .

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