262 = ( 2(x+7))2+(2x)2

Sure, let's solve the equation step by step:

262 = (2(x+7))^2 + (2x)^2

First, let's expand the squares:

262 = 4(x+7)^2 + 4x^2

Divide the entire equation by 4 to simplify:

65.5 = (x+7)^2 + x^2

Expand the square on the left side:

65.5 = x^2 + 14x + 49 + x^2

Combine like terms:

65.5 = 2x^2 + 14x + 49

Subtract 65.5 from both sides to set the equation to zero:

0 = 2x^2 + 14x - 16.5

Divide the entire equation by 2 to simplify:

0 = x^2 + 7x - 8.25

Now, we have a quadratic equation in the form of ax^2 + bx + c = 0. We can solve for x using the quadratic formula, x = [-b ± sqrt(b^2 - 4ac)] / (2a):

x = [-7 ± sqrt((7)^2 - 4*(-8.25))] / (2*1)

Calculate the discriminant (b^2 - 4ac):

Discriminant = (7)^2 - 4*(-8.25) = 49 + 33 = 82

Substitute the discriminant back into the formula:

x = [-7 ± sqrt(82)] / 2

So, the solutions for x are:

x = [-7 + sqrt(82)] / 2 and x = [-7 - sqrt(82)] / 2

These are the solutions for the equation.