xsquared + (x+7)squared = (2x+1)squared, what is x?

x^2 + (x+7)^2 = (2x+1)^2
First expand the brackets. The expansion of the binomial (a+b)^2 = a^2 + 2ab + b^2.
x^2 + (x^2 + 14x + 49) = (4x^2 + 4x + 1)
2x^2 + 14x + 49 = 4x^2 + 4x + 1
Move all terms to the left side. Remember to switch signs as you switch sides.
2x^2 - 4x^2 + 14x - 4x + 49 - 1 = 0
-2x^2 + 10x + 48 = 0
Divide every term by -2. This will make later steps a little easier.
x^2 - 5x - 24 = 0
Think of two numbers that multiply to -24 (thus their signs are opposite) and add to -5. This tells me that the two numbers, ignoring their signs, have a difference of 5 and the larger value is negative. This works for 3 and -8.
(x+3)(x-8) = 0
A product of 0 only happens when one of its factors is 0. Therefore,
x + 3 = 0 OR x - 8 = 0
x = -3 or x = 8

x² + (x+7)² = (2x+1)²
x² + x²+14x+49 = 4x²+4x + 1
2x² - 10x - 48 = 0
x² - 5x -24 = 0
(x-8)(x+3) = 0
x = 8, -3

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x + 2 x + x = 160 Add like terms 4 x = 160 Divide by 4 on each side... x = 40

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RE:
xsquared + (x+7)squared = (2x+1)squared, what is x?
sorry i had to write the squared bit.

x² + (x + 7)(x + 7) = (2x + 1)(2x + 1)
x² + x² + 14x + 49 = 4x² + 4x + 1
0 = 2x² - 10x - 48
0 = x² - 5x - 24
0 = (x - 8)(x + 3)
x = 8 , x = - 3

x^2 + (x+7)^2 = (2x+1) ^2
x^2 + x^2 + 14x + 49 = 4x^2 + 4x + 1 (Foil)
2x^2 + 14x + 49 = 4x^2 + 4x + 1 (Simplify)
-2x^2 + 10x + 48 = 0 (Combine like terms)
x^2 - 5x - 24 = 0 (Divide by -2 to get x^2 by itself)
(x - 8)(x + 3) = 0 (Factor)
x = 8 or -3.

x^2 + (x + 7)^2 = (2x + 1)^2
x^2 + (x + 7)(x + 7) = (2x + 1)(2x + 1)
x^2 + x*x + 7*x + x*7 + 7*7 = 2x*2x + 1*2x + 2x*1 + 1*1
x^2 + x^2 + 7x + 7x + 49 = 4x^2 + 2x + 2x + 1
2x^2 - 4x^2 + 14x - 4x + 49 - 1 = 0
-2x^2 + 10x + 48 = 0
(-2x^2 + 10x + 48)/-2 = 0/-2
x^2 - 5x - 24 = 0
x^2 + 3x - 8x - 24 = 0
(x^2 + 3x) - (8x + 24) = 0
x(x + 3) - 8(x + 3) = 0
(x + 3)(x - 8) = 0

x + 3 = 0
x = -3

x - 8 = 0
x = 8

∴ x = -3 , 8

x^2+(x+7)^2=(2x+1)^2
x^2 + x^2+14x+49= 4x^2+4x+1
2x^2-4x^2+14x-4x+49-1=0
-2x^2+10x+48=0
Divide all terms by -2
x^2-5x-24=0
(x-8)(x+3)=0
Either x-8=0 so x=8, or
x+3=0 and so x= -3

x is either 8 or -3. If you can only have a positive answer, then the answer is just 8

Expanding
x^2+x^2+14x+49=4x^2+4x+1
Simplifying
So:
2x^2-10x -48=0
Dividing by 2
x^2 - 5x - 24-=0
analyzing :
(x-8)(x+3)=0
Either x = 8
oe x = -3