How do you solve #10x^2+9=499#?

2 Answers
Mar 29, 2018

Answer:

#x = +- 7#

Explanation:

Given   #10x^2+9=499#    Solve for #x#

1) Subtract #9# from both sides to isolate the #10x^2# term

#10x^2=490#

2) Divide both sides by #10# to make the numbers smaller

#x^2 = 49#

3) Find the square roots of both sides

#x = +- 7# #larr# answer

---------- Check ----------

Sub in #7# (or #-7#) in the place of #x# in the original equation

#10   x^2 +9=499#
#10 (7^2)+9=499# ?

Clear the exponent by squaring the #7#
#10(49) + 9 = 499# ?

Clear the parentheses
#490 + 9 = 499# ?

Combine like terms
#499 = 499#

#Check#

Mar 29, 2018

Answer:

x1 = 7.53
x2 = - 6.63

Explanation:

y = 10x^2 + 9x = 499
Use the improved quadratic formula (Socratic search):
#D = d^2 = b^2 - 4ac = 81 + 19,960 = 20,041#.
#d = +- 141.57#
There are 2 real roots:
#x = -b/(2a) +- d/(2a) = - 9/20 +- 141.57/20#
#x = (9 +- 141.57)/20#
#x1 = 150.57/20 = 7.53#
#x2 = - 132.57/20 = - 6.63#
graph{10x^2 +9x - 499 [-320, 320, -160, 160]}