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

Question

Isaiah Anthony · Accepted Answer

See a solution process below:

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# According to the quadratic formula, 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# To the closest hundredth, rounded off.

Abigail Allen · Answer

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

Kennedy Adams · Answer

undefined To solve $4.8x^2 = 5.2x + 2.7$ using the quadratic formula, first, rewrite the equation in the form $ax^2 + bx + c = 0$. Then, identify $a$, $b$, and $c$. Finally, apply the quadratic formula:

Given equation: $4.8x^2 - 5.2x - 2.7 = 0$

Using the quadratic formula: $x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$

Substitute the coefficients $a = 4.8$, $b = -5.2$, and $c = -2.7$ into the quadratic formula:

$x = \frac{{-(-5.2) \pm \sqrt{{(-5.2)^2 - 4 \cdot 4.8 \cdot (-2.7)}}}}{{2 \cdot 4.8}}$

Simplify the expression under the square root and then calculate:

$x = \frac{{5.2 \pm \sqrt{{27.04 + 51.84}}}}{{9.6}}$

$x = \frac{{5.2 \pm \sqrt{{78.88}}}}{{9.6}}$

$x = \frac{{5.2 \pm 8.88}}{{9.6}}$

This results in two possible solutions:

$x_1 = \frac{{5.2 + 8.88}}{{9.6}}$

$x_2 = \frac{{5.2 - 8.88}}{{9.6}}$

Calculate the values:

$x_1 \approx 1.4771$

$x_2 \approx -0.3271$

Therefore, the solutions to the equation are approximately $x \approx 1.4771$ and $x \approx -0.3271$.