Final answer:
To solve for x in various equations, such as those involving square roots or quadratics, you can use properties of exponents, take square roots, rearrange the equation, or use the quadratic formula. In some instances involving weak acid dissociation, assumptions can simplify the equation so that x can be easily calculated without complex methods.
Step-by-step explanation:
To solve for x in an equation such as x² = √x, we recognize that the expression √x can be represented as x raised to the power of 1/2, because if you square √x (multiply it by itself), you get x. Moving on to another example, solving a quadratic equation like (2x)² = 4.0 (1 − x)² involves taking the square root of both sides, which simplifies the equation to (2x)(1 − x). After rearrangement, you can then solve for the value of x.
Another form of a quadratic equation that can be solved using the quadratic formula is x²+ +1.2 x 10⁻²x -6.0 × 10⁻³ = 0. However, in some cases, like when dealing with weak acids and their dissociation, assuming x << initial concentration can simplify the equation considerably.
For instance, if an acid has an initial concentration of 0.534 M and a very small dissociation constant, we can approximate that the change in concentration due to the ionization, x, is small enough to be negligible, simplifying the denominator term to just 0.534.