How do you solve $x^2 - 4x + 1 = 0$ using the quadratic formula?

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Answer 1 · 2017-08-09T10:21:57

See a solution process below:

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:

$color(red)(1)$ for $color(red)(a)$

$color(blue)(-4)$ for $color(blue)(b)$

$color(green)(1)$ for $color(green)(c)$ gives:

$x = (-color(blue)((-4)) +- sqrt(color(blue)((-4))^2 - (4 * color(red)(1) * color(green)(1))))/(2 * color(red)(1))$

$x = (color(blue)(4) +- sqrt(color(blue)(16) - 4))/2$

$x = (color(blue)(4) +- sqrt(12))/2$

$x = (color(blue)(4) - sqrt(4 * 3))/2$ and $x = (color(blue)(4) + sqrt(4 * 3))/2$

$x = (color(blue)(4) - sqrt(4)sqrt(3))/2$ and $x = (color(blue)(4) + sqrt(4)sqrt(3))/2$

$x = (color(blue)(4) - 2sqrt(3))/2$ and $x = (color(blue)(4) + 2sqrt(3))/2$

$x = color(blue)(4)/2 - (2sqrt(3))/2$ and $x = color(blue)(4)/2 + (2sqrt(3))/2$

$x = 2 - sqrt(3)$ and $x = 2 + sqrt(3)$

How do you solve x^2 - 4x + 1 = 0 x^2 - 4x + 1 = 0 using the quadratic formula?