Find all real solutions of this equation to answer
the question.
(6 - 2x)(3 - 2x)x = 40

x=4

Step-by-step explanation:

1) Distribute x through the parenthesis: (6x-2x^2)*(3-2x)=40

2) Multiply the parentheses: 18x-12x^2-6x^2+4x^3=40

3) Collect the like terms: 18x-18x^2+4x^3=40

4) Divide the both sides of the equation by 2: 9x-9x^2+2x^3=20

5) Move the constant to the left and change its sign: 9x-9x^2+2x^3-20=0

6) Use the commutative property to reorder the terms: 2x^3-9x^2+9x-20=0

7) Write -9x^2 as a difference: 2x^3-8x^2-x^2+9x-20=0

8) Write 9x as a sum: 2x^3-8x^2-x^2+4x+5x-20=0

9) Factor out 2x^2 from the expression: 2x^2(x-4)-x^2+4x+5x-20=0

10) Factor out -x from the expresstion: 2x^2(x-4)-x(x-4)+5x-20=0

11) Factor out 5 from the expression: 2x^2(x-4)-x(x-4)+5(x-4)=0

12) Factor out x-4 from the expression: (x-4)(2x^2-x+5)=0

13) When the product of factors equals 0, at least one factor is 0:

x-4=0

2x^2-x+5=0

14) Solve the equation for x:

x=4

x≠R

15) Find the union: x=4

C) No. The only real solution is x = 4. It is not possible to cut squares of this size.

Step-by-step explanation:

77

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4