Final answer:
To solve a simplified equation that is an identity like 4(a+b) = 4a + 4b, no actual solving is needed as it holds true for all values. For quadratic equations, the quadratic formula is applied when we have values for a, b, and c. When solving for one unknown, use an equation with all other variables known to find the solution.
Step-by-step explanation:
To solve the simultaneous equations for the unknowns, a series of algebraic steps must be followed carefully. Assuming there is a typo and the intended equation is 4(a+b) = 4a + 4b, we can simplify this through the distributive property and find that it's an identity, meaning it's true for all values of a and b because 4a + 4b is equal to 4a + 4b.
In cases where we have true quadratic equations, for instance of the form at² + bt + c = 0, the quadratic formula, -b ± √(b² - 4ac) / (2a), can be used to find solutions for t. This applies when we have values for a, b, and c, such as in an example where a = 1, b = 0.0211, and c = -0.0211, leading us to use the quadratic formula.
When solving for a variable like w without involving another unknown like t, we would use an equation that contains all known variables besides w. An example is w² = w0² + 2a0, which allows solving for w when values for wo and a0 are known.