# Solve for x: x^2 + (x + 4)^2 = (x + 8)^2

Asked on by loishy

durbanville | High School Teacher | (Level 2) Educator Emeritus

Posted on

Solve: `x^2 + (x+4)^2 = (x+8)^2`

multiply out the brackets:

`x^2 + (x+4)(x+4) = (x+8)(x+8)`

Remember to multiply each factor inside the first bracket by both in the second:

`x^2 + x^2 + 4x+4x+16= x^2+8x+8x+64`

Combine like terms and take everything to the one side:

`therefore x^2+x^2+8x+16 - x^2-16x-64=0`

Combine like terms:

`therefore x^2 -8x -48 = 0`

Now use the factors from the first term (that is, `x times x)` and the factors from the 3rd term which suit this equation (`12 times 4)` to render the middle term of -8x.

`therefore (x-12)(x+4) = 0` Now each factor = 0

`therefore x=12 or x=-4`

Ans: x=12 or x=-4

oldnick | (Level 1) Valedictorian

Posted on

`x^2+(x+4)^2=(x+8)^2`

`x^2+(x+4)^2-(x+8)^2=0`

`x^2=[(x+4)+(x+8)][(x+4)-(x+8)]`

`x^2-8(x+6)=0`

`x^2-8x-48=0`

`x^2 -8x +16-48=16`

`x^2-8x+16=64`

`(x-4)^2=64```

`x-4=+-8`

`x=4+-8`

`x_1=12`    `x_2=-4`

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