Question

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

Answer 1

`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`

Answer 2

`(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)