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we can multiply the terms on each side by the same number, and the terms will remain equal. Therefore, if we multiply the fraction on each side by the product of the denominators of both sides— bd —we get =.
This counterintuitive result occurs because in the case where =, multiplying both sides by multiplies both sides by zero, and so necessarily produces a true equation just as in the first example. In general, whenever we multiply both sides of an equation by an expression involving variables, we introduce extraneous solutions wherever that ...
Multiply each side by . Add to both sides to complete the square. Take the square root of both sides. Isolate . Applying this method to a generic quadratic equation with symbolic coefficients yields the quadratic formula:
For example, multiplying the lengths (in meters or feet) of the two sides of a rectangle gives its area (in square meters or square feet). Such a product is the subject of dimensional analysis. The inverse operation of multiplication is division. For example, since 4 multiplied by 3 equals 12, 12 divided by 3 equals 4.
To solve this kind of equation, the technique is add, subtract, multiply, or divide both sides of the equation by the same number in order to isolate the variable on one side of the equation. Once the variable is isolated, the other side of the equation is the value of the variable. [ 37 ]
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Multiplying or dividing both sides of an equation by a non-zero quantity. Applying an identity to transform one side of the equation. For example, expanding a product or factoring a sum. For a system: adding to both sides of an equation the corresponding side of another equation, multiplied by the same quantity.
Both of these methods have the potential to have the options exercised against you, forcing you to make good on the promise to buy or sell the underlying stock, depending on the type of option.