\[{(x+5)}^{2}={(x-1)}^{2}+48\]

1
Expand.
x2+10x+25=x22x+1+48{x}^{2}+10x+25={x}^{2}-2x+1+48

2
Simplify  x22x+1+48{x}^{2}-2x+1+48  to  x22x+49{x}^{2}-2x+49.
x2+10x+25=x22x+49{x}^{2}+10x+25={x}^{2}-2x+49

3
Cancel x2{x}^{2} on both sides.
10x+25=2x+4910x+25=-2x+49

4
Subtract 2525 from both sides.
10x=2x+492510x=-2x+49-25

5
Simplify  2x+4925-2x+49-25  to  2x+24-2x+24.
10x=2x+2410x=-2x+24

6
Add 2x2x to both sides.
10x+2x=2410x+2x=24

7
Simplify  10x+2x10x+2x  to  12x12x.
12x=2412x=24

8
Divide both sides by 1212.
x=2412x=\frac{24}{12}

9
Simplify  2412\frac{24}{12}  to  22.
x=2x=2

Done

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