Question

Solve for x

write the smaller solution first, and the larger second
5x^2+3=83

smaller x=

larger x=

Answer 1

x= 4

x= -4

explanation:

5x^2+3=83

subtract 3 from both sides

5x^2-80=0

divide both sides by 5

x^2-16=0

consider x^2-16. rewrite x^2-16 as x^2-4^2. The difference of squares can be factored using the rule: a^2-b^2= (a-b)(a+b)

(x-4)(x+4)=0

to find the solutions, solve x

x-4=0 and x+4=0

for the first equation add 4 from both sides

x= 4

x+4=0

for the second equation, subtract both sides by 4

x= -4

------------

x= 4

x= -4

------------

Answer 2

x = {-4, 4}

Explanation:

Subtracting 3 gives ...

5x^2 = 80

Dividing by 5, we get ...

x^2 = 16

Taking the square root gives the solutions ...

x = ±4

The smaller value of x is -4; the larger value is 4.