Applications of Polynomials Equations and Functions. Help Please I am totally lost.?

Question

solve
14= x(x-5)
and
x((5+12x)=28

If you could please tell me the process of how to get the answer I would be very grateful. Thanks in advance.

Answer 1

For the first equation you need to expand it and get all the terms on one side so it is x^2-5x-14=0 when the coefficient in front of x^2 is 1 it is easy to factor, you need to find two numbers that multiply to -14 and add up to -5 this takes a lot of practice to be able to do fast you also need to recognize that the larger number in this case has to be negative and the smaller number is positive. In this case the answer is -7 and 2. So it simplifies to (x-7)(x+2)=0 so the values for x that solve the equation are -2 and 7.

Answer 2

Hi,
First use the properties of equality to get the equation in standard form; then factor it. Next, set each factor = 0 and solve for the values of x that make the individual factor equal to zero.. Let’s do it step-by-step.
First Problem:
Step 1: Use the properties of equality to get the equation in standard form.
x(x-5)=14
x²-5x = 14 (Multiply each term inside the parentheses by x. Distributive property.)
x²-5x-14 = 0….(Put in standard form.)

Step 2: Factor the equation:
x²-5x-14 = 0
(x-7)(x+2)= 0 (Find two factor of -14 whose sum is -5. That’s -7 and 2.)

Step 3: solve for the values of x that make the factor equal to zero.
x-7 = 0
x=7
x+2=0
x=-1

Second Problem: Problem:
Step 1: Use the properties of equality to get the equation in standard form.
x(5+12x)=28
12x²+ 5x = 28 (Multiply each term inside the parentheses by x. Distributive property.)
12x²+5x-28 = 0….(Put in standard form.)

Step 2: Factor the equation:
12x²+5x-28 = 0 (This is somewhat harder and there are different ways of doing this. One way is to find factors so that the sum of the inside and outside terms of the factors =5. For example if we have (ax +b)(cx+d), we want ad +bc =5.
(4x+7)(3x-4)= 0 As you can see, -4*4=-16 and 3*(7) = 21 and -16+ 21 =5.

Step 3: solve for the values of x that make the factor equal to zero.
4x+7 = 0
4x=-7
x=-7/4
3x-4=0
3x=4
x=4/3

Hope this helps.
FE

Answer 3

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