Question

How do you use the quadratic formula to solve `4.8x^2=5.2x+2.7`?

Answer 1

See a solution process below:

Explanation:

First, move each term to the left side of the equation to equate it to `0` while keeping the equation balanced:

`4.8x^2 - color(red)(5.2x) - color(blue)(2.7) = 5.2x - color(red)(5.2x) + 2.7 - color(blue)(2.7)`

`4.8x^2 - 5.2x - 2.7 = 0 + 0`

`4.8x^2 - 5.2x - 2.7 = 0`

The quadratic formula states:

For `ax^2 + bx + c = 0`, the values of `x` which are the solutions to the equation are given by:

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

Substituting `4.8` for `a`; `-5.2` for `b` and `-2.7` for `c` gives:

`x = (-(-5.2) +- sqrt((-5.2)^2 - (4 * 4.8 * -2.7)))/(2 * 4.8)`

`x = (5.2 +- sqrt(27.04 - (-51.84)))/9.6`

`x = (5.2 +- sqrt(27.04 + 51.84))/9.6`

`x = (5.2 +- sqrt(78.88))/9.6`

`x = (5.2 + sqrt(78.88))/9.6` and `x = (5.2 - sqrt(78.88))/9.6`

`x = (5.2 + 8.88)/9.6` and `x = (5.2 - 8.88)/9.6`

`x = 14.08/9.6` and `x = -3.68/9.6`

`x = 1.47` and `x = -0.38`

Rounded to the nearest hundredth.

Answer 2

`x~~1.47` and `x~~-0.38`

Explanation:

A quadratic equation is in the from `ax^2+bx+c=0` where a,b, and c are the numerical coefficients of the unknown variable `x`.

First subtract `-4.8x^2` from both sides of the equation to get one side equal to `0`.

The quadratic formula: `x=(-b+-sqrt(b^2-4ac))/(2a)`
Just insert the respective coefficients into the formula to get

`x=(-5.2+-sqrt(27.04-4(-4.8)2.7))/(-9.6)`

Find the value of the square root:
`x=(-5.2+-sqrt78.88)/(-9.6)` then `x~~(-5.2+-8.88)/(-9.6)`

Solve the fraction separately, once using addition and once subtraction:
`x~~(-5.2+8.88)/(-9.6)` then `x~~-3.68/9.6`

`x~~(-5.2-8.88)/(-9.6)` then `x~~-14.08/-9.6`