Solve each equation by using the quadratic formula: 2x^2-5x=2=0

Question

Please show step by step equation and answer!

Answer 1

I assume the two equations are 2x^2-5x = 2 and 2x^2-5x = 0

Now 2x^2-5x = 2

Subtract 2 from each side.

2x^2-5x-2 = 0

Compare it to quadratic form ax^2+bx+c = 0

a = 2, b = -5, c = -2

Roots are x = [-b±√(b^2-4ac)]/2a

x = [5±√(25+16)]/4

x = [5±√41]/4

Roots are x = (5+√41)/4 and x = (5-√41)/4

Now 2x^2-5x = 0

Compare it to quadratic form ax^2+bx+c = 0

a = 2, b = -5, c = 0

x = [5±√25]/4

x = (5±5)/4

x = 10/4 and x = 0

x = 5/2 and x = 0.

Roots are x = 0 and x = 5/2.