The solution of 3(x^2-14)=(x+1)^2+(x-2)^2+(x-5)^2 is​

Anwer:

3(x  2  −14)=(x+1)  2  +(x−2  )  2+(x−5)  2

Use the distributive property to multiply 3 by x  2  −14.3x  2  −42=(x+1)  2+x−2  1  )  2  +(x−5)  2

Use binomial THEOREM (a+b)  

2

=a  

2

+2ab+b  

2

 to expand (x+1)  

2

.

3x  

2

−42=x  

2

+2x+1+(x−2  

1

)  

2

+(x−5)  

2

Calculate 2 to the power of 1 and get 2.

3x  

2

−42=x  

2

+2x+1+(x−2)  

2

+(x−5)  

2

Use binomial theorem (a−b)  

2

=a  

2

−2ab+b  

2

 to expand (x−2)  

2

.

3x  

2

−42=x  

2

+2x+1+x  

2

−4x+4+(x−5)  

2

Combine x  

2

 and x  

2

 to get 2x  

2

.

3x  

2

−42=2x  

2

+2x+1−4x+4+(x−5)  

2

Combine 2x and −4x to get −2x.

3x  

2

−42=2x  

2

−2x+1+4+(x−5)  

2

Add 1 and 4 to get 5.

3x  

2

−42=2x  

2

−2x+5+(x−5)  

2

Use binomial theorem (a−b)  

2

=a  

2

−2ab+b  

2

 to expand (x−5)  

2

.

3x  

2

−42=2x  

2

−2x+5+x  

2

−10x+25

Combine 2x  

2

 and x  

2

 to get 3x  

2

.

3x  

2

−42=3x  

2

−2x+5−10x+25

Combine −2x and −10x to get −12x.

3x  

2

−42=3x  

2

−12x+5+25

Add 5 and 25 to get 30.

3x  

2

−42=3x  

2

−12x+30

Subtract 3x  

2

 from both sides.

3x  

2

−42−3x  

2

=−12x+30

Combine 3x  

2

 and −3x  

2

 to get 0.

−42=−12x+30

Swap sides so that all variable terms are on the LEFT hand side.

−12x+30=−42

Subtract 30 from both sides.

−12x=−42−30

Subtract 30 from −42 to get −72.

−12x=−72

DIVIDE both sides by −12.

x=  

−12

−72

​  

Divide −72 by −12 to get 6.

x=6

Step-by-step explanation: