What are the approximate solutions of #2x^2 + x = 14# rounded to the nearest hundredth?

2 Answers
Aug 28, 2017

Answer:

#color(green)(x=2.41# or #color(green)(x=-2.91)color(white)("xxx")#(both to the nearest hundrdeth.

Explanation:

Re-writing the given equation as
#color(white)("XXX")color(red)2x^2+color(blue)1xcolor(green)(-14)=0#
and applying the quadratic formula:
#color(white)("XXX")x=(-color(blue)1+-sqrt(color(blue)1^2-4 * color(red)2 * color(green)(""(-14))))/(2 * color(red)2)#

#color(white)("XXXx")=(-1+-sqrt(113))/4#

with the use of a calculator (or, im my case I used a spreadsheet)
#color(white)("XXX")x ~~ 2.407536453color(white)("xxx")orcolor(white)("xxx')x~~-2.9075366453#

Rounding to the nearest hundredths gives the results in the "Answer" (above)

Aug 28, 2017

Answer:

See a solution process below:

Explanation:

First, we can subtract #color(red)(14)# from each side of the equation to put the equation in standard form while keeping the equation balanced:

#2x^2 + x - color(red)(14) = 14 - color(red)(14)#

#2x^2 + x - 14 = 0#

We can now use the quadratic equation to solve this problem.

The quadratic formula states:

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)# for #color(red)(a)#

#color(blue)(1)# for #color(blue)(b)#

#color(green)(-14)# for #color(green)(c)# gives:

#x = (-color(blue)(1) +- sqrt(color(blue)(1)^2 - (4 * color(red)(2) * color(green)(-14))))/(2 * color(red)(2))#

#x = (-color(blue)(1) +- sqrt(1 - (-112)))/4#

#x = (-color(blue)(1) +- sqrt(1 + 112))/4#

#x = (-color(blue)(1) - sqrt(1 + 112))/4# and #x = (-color(blue)(1) + sqrt(1 + 112))/4#

#x = (-color(blue)(1) - sqrt(113))/4# and #x = (-color(blue)(1) + sqrt(113))/4#

#x = (-color(blue)(1) - 10.6301)/4# and #x = (-color(blue)(1) + 10.6301)/4#

#x = -11.6301/4# and #x = 9.6301/4#

#x = -2.91# and #x = 2.41# rounded to the nearest hundredth.