How do you solve #3x^2 + 13x = 10#?

Question

Eva Abramson · Accepted Answer

See a solution process below:

First, subtract #color(red)(10)# from each side of the equation to put the equation in standard quadratic for while keeping the equation balanced: #3x^2 + 13x - color(red)(10) = 10 - color(red)(10)# #3x^2 + 13x - 10 = 0# The quadratic equation can now be used to solve this problem: According to the quadratic formula, 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))# Replacing: #color(red)(3)# for #color(red)(a)# #color(blue)(13)# for #color(blue)(b)# #color(green)(-10)# for #color(green)(c)# gives: #x = (-color(blue)(13) +- sqrt(color(blue)(13)^2 - (4 * color(red)(3) * color(green)(-10))))/(2 * color(red)(3))# #x = (-color(blue)(13) +- sqrt(169 - (12 * color(green)(-10))))/6# #x = (-color(blue)(13) +- sqrt(169 - (-120)))/6# #x = (-color(blue)(13) +- sqrt(169 + 120))/6# #x = (-color(blue)(13) +- sqrt(289))/6# #x = (-color(blue)(13) - 17)/6# and #x = (-color(blue)(13) + 17)/6# #x = -30/6# and #x = 4/6# #x = -5# and #x = 2/3# The Solution Set Is: #x = {-5, 2/3}#

Ethan Adkins · Answer

undefined To solve the equation 3x^2 + 13x = 10, follow these steps:

1. Rewrite the equation in standard form: 3x^2 + 13x - 10 = 0.
2. Use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a), where a = 3, b = 13, and c = -10.
3. Plug in the values of a, b, and c into the quadratic formula.
4. Solve for the two possible values of x by computing the expressions under the square root separately and then finding the two possible values for x by adding and subtracting the square root term.
5. Simplify each expression to find the final solutions for x.