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Solve for x: x^2 + (x + 4)^2 = (x + 8)^2
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High School Teacher
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
Posted by durbanville on May 8, 2013 at 8:46 PM (Answer #1)
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