How do you solve $2.3x^2-1.4x=6.8$ using the quadratic formula?

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Answer 1 · 2017-08-21T12:20:45

See a solution process below:

First, subtract $color(red)(6.8)$ from each side of the equation to put the equation in standard form:

$2.3x^2 - 1.4x - color(red)(6.8) = 6.8 - color(red)(6.8)$

$2.3x^2 - 1.4x - 6.8 = 0$

We can now 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:

$color(red)(2.3)$ for $color(red)(a)$

$color(blue)(-1.4)$ for $color(blue)(b)$

$color(green)(-6.8)$ for $color(green)(c)$ gives:

$x = (-color(blue)((-1.4)) +- sqrt(color(blue)((-1.4))^2 - (4 * color(red)(2.3) * color(green)(-6.8))))/(2 * color(red)(2.3))$

$x = (color(blue)(1.4) +- sqrt(color(blue)(1.96) - (-62.56)))/4.6$

$x = (color(blue)(1.4) +- sqrt(color(blue)(1.96) + 62.56))/4.6$

$x = (color(blue)(1.4) +- sqrt(64.52))/4.6$

$x = (color(blue)(1.4) +- sqrt(4 * 16.13))/4.6$

$x = (color(blue)(1.4) +- sqrt(4)sqrt(16.13))/4.6$

$x = (color(blue)(1.4) +- 2sqrt(16.13))/4.6$

$x = (color(blue)(1.4) - 2sqrt(16.13))/4.6$ and $x = (color(blue)(1.4) + 2sqrt(16.13))/4.6$

$x = (color(blue)((2 * 0.7)) - 2sqrt(16.13))/(2 * 2.3)$ and $x = (color(blue)((2 * 0.7)) + 2sqrt(16.13))/(2 * 2.3)$

$x = (color(blue)(0.7) - sqrt(16.13))/2.3$ and $x = (color(blue)(0.7) + sqrt(16.13))/2.3$

How do you solve 2.3x^2-1.4x=6.82.3x^2-1.4x=6.8 using the quadratic formula?