Processing Math: Done

From Förberedande kurs i matematik 1

Write the equation in normalized form by dividing both sides by 5,

x2+52x−53=0.

Complete the square on the left-hand side,

x2+52x−53=x+2252−2252−53=x+512−512−53=x+512−125−2535=x+512−2516.

The equation is now rewritten as

x+512=2516,

and taking the root gives the solutions

• x+51=2516=54  because 542=2516  which gives x=−51+54=53

• x+51=−2516=−54  which gives x=−51−54=−1.

Finally, we check the answer by substituting x=−1 and x=35 into the equation:

• x = 1:  LHS=5(−1)2+2(−1)−3=5−2−3=0=RHS,

• x = 3/5:  LHS=5532+253−3=5925+56−535=0=RHS.