s^2+27s+34=0

Simple and best practice solution for s^2+27s+34=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 s^2+27s+34=0 equation:


Simplifying
s2 + 27s + 34 = 0

Reorder the terms:
34 + 27s + s2 = 0

Solving
34 + 27s + s2 = 0

Solving for variable 's'.

Begin completing the square.

Move the constant term to the right:

Add '-34' to each side of the equation.
34 + 27s + -34 + s2 = 0 + -34

Reorder the terms:
34 + -34 + 27s + s2 = 0 + -34

Combine like terms: 34 + -34 = 0
0 + 27s + s2 = 0 + -34
27s + s2 = 0 + -34

Combine like terms: 0 + -34 = -34
27s + s2 = -34

The s term is 27s.  Take half its coefficient (13.5).
Square it (182.25) and add it to both sides.

Add '182.25' to each side of the equation.
27s + 182.25 + s2 = -34 + 182.25

Reorder the terms:
182.25 + 27s + s2 = -34 + 182.25

Combine like terms: -34 + 182.25 = 148.25
182.25 + 27s + s2 = 148.25

Factor a perfect square on the left side:
(s + 13.5)(s + 13.5) = 148.25

Calculate the square root of the right side: 12.175795662

Break this problem into two subproblems by setting 
(s + 13.5) equal to 12.175795662 and -12.175795662.

Subproblem 1

s + 13.5 = 12.175795662 Simplifying s + 13.5 = 12.175795662 Reorder the terms: 13.5 + s = 12.175795662 Solving 13.5 + s = 12.175795662 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + s = 12.175795662 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + s = 12.175795662 + -13.5 s = 12.175795662 + -13.5 Combine like terms: 12.175795662 + -13.5 = -1.324204338 s = -1.324204338 Simplifying s = -1.324204338

Subproblem 2

s + 13.5 = -12.175795662 Simplifying s + 13.5 = -12.175795662 Reorder the terms: 13.5 + s = -12.175795662 Solving 13.5 + s = -12.175795662 Solving for variable 's'. Move all terms containing s to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + s = -12.175795662 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + s = -12.175795662 + -13.5 s = -12.175795662 + -13.5 Combine like terms: -12.175795662 + -13.5 = -25.675795662 s = -25.675795662 Simplifying s = -25.675795662

Solution

The solution to the problem is based on the solutions from the subproblems. s = {-1.324204338, -25.675795662}

See similar equations:

| 8+12x=15x | | -15+5b=-5(b+5) | | 577=226-3c | | 4z^2-64z-60=0 | | x^3+y^3=z^3+1 | | x(2x+7)=-55 | | 3y^2+42y=93 | | 7/8y-1/4=-1/8y-1/2 | | h^2+h=7 | | -3j^2-90j=-69 | | 1OZ= | | 1/3y-3/4=2/3y-1/2 | | 4v^2+4v-116=0 | | 9(z-6)=4(z+6) | | 652=67+5r | | 24+7n=6(7n+4) | | 5z+2-3z=2+z+10 | | 5x+-7=x | | q^2-15q=-46 | | 3+x-x^2=0 | | x-9y=57 | | k^2+8k-1=0 | | 16+x-x^2=0 | | -4n-2=-6n-14 | | -2p^2+46p=-48 | | 11(b+18)-6(2b+1)=4(-b+9) | | (32x+70)=(20x+6) | | -2f^2-28f+94=0 | | 3y+12=14 | | 3y+5+2y-7+27= | | x^2-3x+1=2x | | 4(-b+9)= |

Equations solver categories