How do you solve 2x^2 = 14x + 20?

2 Answers
Apr 20, 2018

x = (7 +- sqrt(89))/2

Explanation:

=> 2x^2 = 14x + 20

Divide both sides by 2

=> x^2 = 7x + 10

Rearrange the equation

=> x^2 - 7x - 10 = 0

It’s in the form of ax^2 + bx + c = 0

where,

  • a = 1
  • b = -7
  • c = -10

Use formula for quadratic equation to find x

x = (-b +- sqrt(b^2 - 4ac))/(2a)

x = (-(-7) +- sqrt((-7)^2 - (4 × 1 × -10)))/(2 × 1)

x = (7 +- sqrt(49 + 40))/2

x = (7 +- sqrt(89))/2

Apr 20, 2018

(7\pm\sqrt(89))/2

Explanation:

  • Move everything to left side: 2x^2-14x-20=0
  • Factor out a 2: 2(x^2-7x-10)=0
  • Solve the parenthetical quadratic (see here for steps)