Square root 80 = 4 x square root 5
because root 80 = root 16 x root 5
- Factoring a quadratic equation can be defined as the process of breaking the equation into the product of its factors.
![\:❏ \: \: \LARGE{\rm{{{\color{orange}{6 {x }^{2} \: + \: 7x \: - 3}}}}}](https://tex.z-dn.net/?f=%20%5C%3A%E2%9D%8F%20%5C%3A%20%20%20%5C%3A%20%5CLARGE%7B%5Crm%7B%7B%7B%5Ccolor%7Borange%7D%7B6%20%7Bx%20%7D%5E%7B2%7D%20%20%5C%3A%20%20%2B%20%20%5C%3A%207x%20%5C%3A%20%20-%203%7D%7D%7D%7D%7D)
- Factorize the equation by breaking down the middle term.
![\large \blue\implies \tt \large \: 6 {x }^{2} \: + \: 7x \: - 3](https://tex.z-dn.net/?f=%20%5Clarge%20%20%5Cblue%5Cimplies%20%5Ctt%20%5Clarge%20%5C%3A%206%20%7Bx%20%7D%5E%7B2%7D%20%20%5C%3A%20%20%2B%20%20%5C%3A%207x%20%5C%3A%20%20-%203)
- Let’s identify two factors such that their sum is 7 and the product is -18.
Sum of two factors = 7 = 9 - 2
Product of these two factors = 9 × (-2) = 18
- Now, split the middle term.
![\large \blue\implies \tt \large \:6 {x}^{2} \: + \: 9x \: - \: 2x \: - \: 3](https://tex.z-dn.net/?f=%5Clarge%20%20%5Cblue%5Cimplies%20%5Ctt%20%5Clarge%20%5C%3A6%20%7Bx%7D%5E%7B2%7D%20%5C%3A%20%20%20%2B%20%5C%3A%209x%20%5C%3A%20%20-%20%20%5C%3A%202x%20%5C%3A%20-%20%20%5C%3A%203)
- Take the common terms and simplify.
![\: \\ \large\blue\implies \tt \large \:3x(2x \: + \: 3)\: -1(2x \: + \: 3)](https://tex.z-dn.net/?f=%20%20%5C%3A%20%20%5C%5C%20%5Clarge%5Cblue%5Cimplies%20%5Ctt%20%5Clarge%20%5C%3A3x%282x%20%5C%3A%20%20%2B%20%20%5C%3A%203%29%5C%3A%20-1%282x%20%5C%3A%20%20%2B%20%5C%3A%203%29)
![\\ \large\blue\implies \tt \large \:(3x \: - \:1 ) \quad \: (2x \: + \: 3) \: = \: 0](https://tex.z-dn.net/?f=%20%5C%5C%20%5Clarge%5Cblue%5Cimplies%20%5Ctt%20%5Clarge%20%5C%3A%283x%20%5C%3A%20%20-%20%20%5C%3A1%20%29%20%5Cquad%20%5C%3A%20%282x%20%5C%3A%20%20%2B%20%20%5C%3A%203%29%20%5C%3A%20%20%3D%20%20%5C%3A%200)
Thus, (3x - 1) and (2x + 3) are the factors of the given quadratic equation.
- Solving these two linear factors, we get
![\large\blue\implies \tt \large \:x \: = \: \frac{1}{3} \: \: , \: \: \frac{ - 3}{2} \\](https://tex.z-dn.net/?f=%5Clarge%5Cblue%5Cimplies%20%5Ctt%20%5Clarge%20%5C%3Ax%20%5C%3A%20%3D%20%20%5C%3A%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%5C%3A%20%20%5C%3A%20%2C%20%20%5C%3A%20%20%5C%3A%20%5Cfrac%7B%20-%203%7D%7B2%7D%20%20%5C%5C%20)
A = P(1 + r/n)nt
Amount = Principal (1 + interest rate in decimal form divided by number of times interest is compounded per year)number of years
Amount = $900,000 (1 + 4.8/12)20
Answer:
4.5
Step-by-step explanation:
divide all the equation
look for the lowest common factor which is 2
then multiply out numerators