How do you solve the quadratic using the quadratic formula given #14m^2+1=6m^2+7m#?

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Answer 1 · 2017-08-03T04:19:13

See a solution process below:

First we need to convert the equation to standard form:

#-color(red)(6m^2) + 14m^2 - color(blue)(7m) + 1 = -color(red)(6m^2) + 6m^2 + 7m - color(blue)(7m)#

#(-color(red)(6) + 14)m^2 - 7m + 1 = 0 + 0#

#8m^2 - 7m + 1 = 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)(8)# for #color(red)(a)#

#color(blue)(-7)# for #color(blue)(b)#

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

#x = (-color(blue)((-7)) +- sqrt(color(blue)((-7))^2 - (4 * color(red)(8) * color(green)(1))))/(2 * color(red)(8))#

#x = (color(blue)(7) +- sqrt(color(blue)(49) - 32))/16#

#x = (7 +- sqrt(17))/16#