(X+7)(x-7)=(x+1)2

Solution for (X+7)(x-7)=(x+1)2 equation:

(X+7)(X-7)=(X+1)2

We move all terms to the left:

(X+7)(X-7)-((X+1)2)=0

We use the square of the difference formula

X^2-((X+1)2)-49=0


We calculate terms in parentheses: -((X+1)2), so:

(X+1)2

We multiply parentheses

2X+2

Back to the equation:

-(2X+2)


We get rid of parentheses

X^2-2X-2-49=0

We add all the numbers together, and all the variables

X^2-2X-51=0

a = 1; b = -2; c = -51;
Δ = b2-4ac
Δ = -22-4·1·(-51)
Δ = 208
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{13}}{2*1}=\frac{2-4\sqrt{13}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{13}}{2*1}=\frac{2+4\sqrt{13}}{2}
$