4s^2+12s-9=0

Simple and best practice solution for 4s^2+12s-9=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 4s^2+12s-9=0 equation:


Simplifying
4s2 + 12s + -9 = 0

Reorder the terms:
-9 + 12s + 4s2 = 0

Solving
-9 + 12s + 4s2 = 0

Solving for variable 's'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-2.25 + 3s + s2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + 3s + 2.25 + s2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + 3s + s2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + 3s + s2 = 0 + 2.25
3s + s2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
3s + s2 = 2.25

The s term is 3s.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3s + 2.25 + s2 = 2.25 + 2.25

Reorder the terms:
2.25 + 3s + s2 = 2.25 + 2.25

Combine like terms: 2.25 + 2.25 = 4.5
2.25 + 3s + s2 = 4.5

Factor a perfect square on the left side:
(s + 1.5)(s + 1.5) = 4.5

Calculate the square root of the right side: 2.121320344

Break this problem into two subproblems by setting 
(s + 1.5) equal to 2.121320344 and -2.121320344.

Subproblem 1

s + 1.5 = 2.121320344 Simplifying s + 1.5 = 2.121320344 Reorder the terms: 1.5 + s = 2.121320344 Solving 1.5 + s = 2.121320344 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + s = 2.121320344 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + s = 2.121320344 + -1.5 s = 2.121320344 + -1.5 Combine like terms: 2.121320344 + -1.5 = 0.621320344 s = 0.621320344 Simplifying s = 0.621320344

Subproblem 2

s + 1.5 = -2.121320344 Simplifying s + 1.5 = -2.121320344 Reorder the terms: 1.5 + s = -2.121320344 Solving 1.5 + s = -2.121320344 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + s = -2.121320344 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + s = -2.121320344 + -1.5 s = -2.121320344 + -1.5 Combine like terms: -2.121320344 + -1.5 = -3.621320344 s = -3.621320344 Simplifying s = -3.621320344

Solution

The solution to the problem is based on the solutions from the subproblems. s = {0.621320344, -3.621320344}

See similar equations:

| 0.3x=x-140 | | -5-(15-1)=2(7x-16)-x | | -2x^2+6x-10=0 | | X+18+4x=-42-4x-48 | | 6t^2=-18t | | 4x^2-5x+8=0 | | (5b-3)(5b+3)=0 | | 15x+22=-7+66 | | X+21+3x=-22-3x-27 | | x+(x-4)=4 | | x-2+8=13 | | 5x^2-10x-15=0 | | a=12345678910/1234567890-1(12345678910)+12345678910(12345678910) | | 3(x^2+1)-6x=0 | | 4y+12=80 | | 36x^3-28x^2+9x-7= | | a^2+9a-22=0 | | 12345678910(12345678910)=12345678910-12345678910(12345678910) | | 8b^2+4b= | | h^2-19h+90=0 | | 11k-15=18 | | m-(-26.1)=32 | | m-(-26.1)= | | 7x^2+10x-9=0 | | 9a-13=59 | | 3(12-2x)-10(2x-6)=-60 | | x^2-4x-27.25=0 | | a+6= | | 3x=3+y | | 4x^2+2x-3=0 | | 5a-2=a+6 | | 2+6=1-3c |

Equations solver categories