Question

What are the approximate solutions of 4x^2 + 3 = -12x to the nearest hundredth

Answer 1

Approximate solutions are

X subset 2 is approximately equal to -2.72

X subset 1 is approximately equal to -0.28

Answer 2

Hello from MrBillDoesMath!

Answer: -.28 and -2.72

Discussion:

This is a quadratic equation (where a = 4, b +12, and c = 3 using the standard notation involved in the solution)

4x^2 + 3= -12x => (given). Add 12x to both sides

4x^2 + 12x + 3 = 0.

From the quadratic formula:

x = ( -12 +\- sqrt ( 12^2 - 4(4)(3) ) )/ (2 * 4)

x = ( -12 +\- sqrt (144 -48))/ (2 * 4)

x = ( -12 +\- sqrt (96)) / (2 * 4)

x = ( -12 +\- sqrt(16*6) ) / (2 * 4)

The "+" solution, x = -12/8 + ( 4 /8)sqrt(6) = -3/2 + 1/2 (sqrt(6)) = -.28

The "-" solution x = -12/8 - ( 4 /8)sqrt(6) = -3/2 - 1/2 (sqrt(6)) = -2.72

Regards,

MrB