Question

Solve for x in the equation x2-5x+1=3

Answer 1

`x^(2) -5x+1=3`

The first thing you should do to solve is set the equation equal to zero. Subtract 3 from each side:


`x^(2) -5x+1=3 \\ \\ x^(2) -5x-2=0`

The resulting equation doesn't seem to be factorable. To solve for x, use the quadratic formula:


`x= (-b \pm √(b^2-4ac) )/(2a) \\ \\ x= (-(-5) \pm √((-5)^2-4(1 )(-2)) )/(2(1)) \\ \\ x= (5 \pm √(25-4(-2)) )/(2) \\ \\ x= (5 \pm √(25+8) )/(2) \\ \\ x= (5 \pm √(33) )/(2) \\ \\ x \approx (5 \pm 5.74)/(2) \\ \\ \\ \\ x \approx (5+5.74)/(2) \\ \\ x \approx (10.74)/(2) \\ \\ x \approx 5.37 \\ \\ \\ \\ x \approx (5-5.74)/(2) \\ \\ x \approx (-0.74)/(2) \\ \\ x \approx -0.37`

To the nearest hundredths place, the solutions to the original equation are x = 5.37 and x = -0.37.