How to solve this equation?

5(x+1)² + 7(x+3)² = 12(x+2)²

2 Answers
Jun 23, 2018

x=-5x=5

Explanation:

Solve:

5(x+1)^2+7(x+3)^2=12(x+2)^25(x+1)2+7(x+3)2=12(x+2)2

Expand using the sum of squares: (a+b)^2=a^2+2ab+b^2(a+b)2=a2+2ab+b2, or using the FOIL method: https://www.ipracticemath.com/learn/algebra/foil-method-of-binomial-multiplication

5(x^2+2x+1)+7(x^2+6x+9)=12(x^2+4x+4)5(x2+2x+1)+7(x2+6x+9)=12(x2+4x+4)

Expand using the distributive property: a(b+c)=ab+aca(b+c)=ab+ac

5x^2+10x+5+7x^2+42x+63=12x^2+48x+485x2+10x+5+7x2+42x+63=12x2+48x+48

Collect like terms.

(5x^2+7x^2)+(10x+42x)+(5+63)=12x^2+48x+48(5x2+7x2)+(10x+42x)+(5+63)=12x2+48x+48

Combine like terms.

12x^2+52x+68=12x^2+48x+4812x2+52x+68=12x2+48x+48

Cancel 12x^212x2 on both sides.

color(red)cancel(color(black)(12x^2))+52x+68=color(red)cancel(color(black)(12x^2))+48x+48

Simplify.

52x+68=48x+48

Subtract 48x from both sides.

52x-48x+68=48

Simplify.

4x+68=48

Subtract 68 from both sides.

4x=48-68

Simplify.

4x=-20

Divide both sides by 4.

x=-20/4

Simplify.

x=-5

Jun 23, 2018

x = -5

Explanation:

Step by step, performing legal algebraic operations that just happen to simplify the expression:

5(x+1)^2 + 7(x+3)^2 = 12(x+2)^2

5(x^2+2x+1) + 7(x^2+6x+9) = 12(x^2+4x+4)

(5x^2+10x+5) + (7x^2+42x+63) = (12x^2+48x+48)

(12x^2+52x+68) = (12x^2+48x+48)

(12x^2+52x+68) - (12x^2+48x+48) = 0

(0x^2+4x+20) = 0

4x+20 = 0

4x = -20

1/cancel(4) * cancel(4)x = 1/cancel(4) * (-cancel(20)^5)

x = -5

I hope this helps,
Steve