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[tex]\huge\sf\blue{·˚₊·➳answer°.}[/tex]

1a. To determine the solution set of the quadratic equation x² - 28x + 168 = 0 by factoring, we can factorize the equation as [tex]\large\sf\purple{(x \:-\: 14)(x \:-\: 12) \:= \:0}[/tex].

[tex]\boxed{\sf\pink{✓}}[/tex] The solutions are [tex]\large\sf\pink{x\: =\: 14}[/tex] and [tex]\large\sf\pink{x\: =\: 12}[/tex].

1b. To determine the solution set of the quadratic equation 3x² + 26x + 168 = 2x², we need to rearrange the equation to bring all terms to one side: [tex]\large\sf\purple{x² \:+\: 26x \:-\: 168\: = \:0}[/tex].

Then, we can factorize it as [tex]\large\sf\purple{(x\: + \:14)(x \:- \:12)\: =\: 0}[/tex].

[tex]\boxed{\sf\pink{✓}}[/tex]The solutions are [tex]\large\sf\pink{x\: = \:-14}[/tex] and [tex]\large\sf\pink{x\: =\: 12}[/tex].

2. To find the solutions to quadratic equations, we can use different methods such as factoring, completing the square, or using the quadratic formula. Factoring involves breaking down the equation into factors and setting each factor equal to zero. Completing the square involves manipulating the equation to create a perfect square trinomial, which can be solved by taking the square root. The quadratic formula is a general formula that can be used for any quadratic equation. It states that the solutions can be found using the formula x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation in the form ax² + bx + c = 0. Depending on the equation and the given information, we can choose the most suitable method to find the solutions.

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