$\text{a)}{\left(7-x\right)}^2=x^2+7$  

$49-14x+x^2=x^2+7$  

$49-14x=7$  

$-14x=-42\mid :\left(-14\right)$  

$x=3$  

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$\text{b)}{\left(5x+2\right)}^2=25x^2$  

$25x^2+20x+4=25x^2$  

$20x+4=0$  

$20x=-4\mid :20$  

$x=-\frac{1}{5}$  

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$\text{c)}{\left(x+4\right)}^2={\left(6-x\right)}^2$  

$x^2+8x+16=36-12x+x^2$  

$8x+16=36-12x$  

$20x=20\mid :20$  

$x=1$  

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$\text{d)}{\left(x-15\right)}^2={\left(x-11\right)}^2$  

$x^2-30x+225=x^2-22x+121$  

$-30x+225=-22x+121$  

$-8x=-104\mid :\left(-8\right)$  

$x=13$