How do you use the quadratic formula to solve $2.5x^2-2.8x=0.4$ ?

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Answer 1 · 2017-08-20T17:16:45

See a solution process below:

First, subtract $color(red)(0.4)$ from each side of the equation to put the equation in standard form while keeping the equation balanced:

$2.5x^2 - 2.8x - color(red)(0.4) = 0.4 - color(red)(0.4)$

$2.5x^2 - 2.8x - 0.4 = 0$

Now we can use the quadratic equation to solve this problem:

For $color(red)(a)x^2 + color(blue)(b)x + color(green)(c) = 0$ , the values of $x$ which are the solutions to the equation are given by:

$x = (-color(blue)(b) +- sqrt(color(blue)(b)^2 - (4color(red)(a)color(green)(c))))/(2 * color(red)(a))$

Substituting:

$color(red)(2.5)$ for $color(red)(a)$

$color(blue)(-2.8)$ for $color(blue)(b)$

$color(green)(-0.4)$ for $color(green)(c)$ gives:

$x = (-color(blue)((-2.8)) +- sqrt(color(blue)((-2.8))^2 - (4 * color(red)(2.5) * color(green)(-0.4))))/(2 * color(red)(2.5))$

$x = (2.8 +- sqrt(7.84 - 4))/5$

$x = (2.8 +- sqrt(3.84 - 4))/5$

How do you use the quadratic formula to solve 2.5x^2-2.8x=0.42.5x^2-2.8x=0.4?