Question

How do you use the quadratic formula to solve `3/4(x-1)^2=-4/3x+4/5`?

Answer 1

Before one uses the quadratic formula, one must write the equation in the form:

`ax^2+bx+c=0`

Then substitute, a, b, and c into the formula:

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

Explanation:

Given: `3/4(x-1)^2=-4/3x+4/5`

Multiply both sides of the equation by the factors: `(3)(4)(5)`

`45(x-1)^2=-80x+48`

Expand the square:

`45(x^2-2x+1) = -80x +48`

Distribute the 45:

`45x^2-90x+45 = -80x +48`

Combine like terms:

`45x^2-10x-3 = 0`

By observation, `a =45, b = -10, and c = -3`

Substitute into the formula:

`x = (10+-sqrt((-10)^2-4(45)(-3)))/(2(45))`

`x = (10+-sqrt(640))/90`

`x = (10+-8sqrt(10))/90`

`x = (10-8sqrt10)/90` and `x = (10+8sqrt10)/90`