How do you use the quadratic formula to solve #4.8x^2=5.2x+2.7#?

2 Answers
Jun 28, 2017

Answer:

See a solution process below:

Explanation:

First, move each term to the left side of the equation to equate it to #0# while keeping the equation balanced:

#4.8x^2 - color(red)(5.2x) - color(blue)(2.7) = 5.2x - color(red)(5.2x) + 2.7 - color(blue)(2.7)#

#4.8x^2 - 5.2x - 2.7 = 0 + 0#

#4.8x^2 - 5.2x - 2.7 = 0#

The quadratic formula states:

For #ax^2 + bx + c = 0#, the values of #x# which are the solutions to the equation are given by:

#x = (-b +- sqrt(b^2 - 4ac))/(2a)#

Substituting #4.8# for #a#; #-5.2# for #b# and #-2.7# for #c# gives:

#x = (-(-5.2) +- sqrt((-5.2)^2 - (4 * 4.8 * -2.7)))/(2 * 4.8)#

#x = (5.2 +- sqrt(27.04 - (-51.84)))/9.6#

#x = (5.2 +- sqrt(27.04 + 51.84))/9.6#

#x = (5.2 +- sqrt(78.88))/9.6#

#x = (5.2 + sqrt(78.88))/9.6# and #x = (5.2 - sqrt(78.88))/9.6#

#x = (5.2 + 8.88)/9.6# and #x = (5.2 - 8.88)/9.6#

#x = 14.08/9.6# and #x = -3.68/9.6#

#x = 1.47# and #x = -0.38#

Rounded to the nearest hundredth.

Jun 28, 2017

Answer:

#x~~1.47# and #x~~-0.38#

Explanation:

A quadratic equation is in the from #ax^2+bx+c=0# where a,b, and c are the numerical coefficients of the unknown variable #x#.

First subtract #-4.8x^2# from both sides of the equation to get one side equal to #0#.

The quadratic formula: #x=(-b+-sqrt(b^2-4ac))/(2a)#
Just insert the respective coefficients into the formula to get

#x=(-5.2+-sqrt(27.04-4(-4.8)2.7))/(-9.6)#

Find the value of the square root:
#x=(-5.2+-sqrt78.88)/(-9.6)# then #x~~(-5.2+-8.88)/(-9.6)#

Solve the fraction separately, once using addition and once subtraction:
#x~~(-5.2+8.88)/(-9.6)# then #x~~-3.68/9.6#

#x~~(-5.2-8.88)/(-9.6)# then #x~~-14.08/-9.6#