Processing Math: Done

From Förberedande kurs i matematik 1

We can simplify the left-hand side in the equation by expanding the squares using the squaring rule

(x+3)2−(x−5)2=(x2+23x+32)−(x2−25x+52)=x2+6x+9−x2+10x−25=16x−16.

Thus, the equation is

16x−16=6x+4.

Now, move all x's to the left-hand side (subtract 6x from both sides) and the constants to the right-hand side (add 16 to both sides)

16x−6x10x=4+16=20.

Divide both sides by 10 to get the answer

x=1020=2.

Finally, we check that x=2 satisfies the equation in the exercise

LHSRHS=(2+3)2−(2−5)2=52−(−3)2=25−9=16=62+4=12+4=16.