6x^2+105x=37

Simple and best practice solution for 6x^2+105x=37 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 6x^2+105x=37 equation:


Simplifying
6x2 + 105x = 37

Reorder the terms:
105x + 6x2 = 37

Solving
105x + 6x2 = 37

Solving for variable 'x'.

Reorder the terms:
-37 + 105x + 6x2 = 37 + -37

Combine like terms: 37 + -37 = 0
-37 + 105x + 6x2 = 0

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

Divide each side by '6'.
-6.166666667 + 17.5x + x2 = 0

Move the constant term to the right:

Add '6.166666667' to each side of the equation.
-6.166666667 + 17.5x + 6.166666667 + x2 = 0 + 6.166666667

Reorder the terms:
-6.166666667 + 6.166666667 + 17.5x + x2 = 0 + 6.166666667

Combine like terms: -6.166666667 + 6.166666667 = 0.000000000
0.000000000 + 17.5x + x2 = 0 + 6.166666667
17.5x + x2 = 0 + 6.166666667

Combine like terms: 0 + 6.166666667 = 6.166666667
17.5x + x2 = 6.166666667

The x term is 17.5x.  Take half its coefficient (8.75).
Square it (76.5625) and add it to both sides.

Add '76.5625' to each side of the equation.
17.5x + 76.5625 + x2 = 6.166666667 + 76.5625

Reorder the terms:
76.5625 + 17.5x + x2 = 6.166666667 + 76.5625

Combine like terms: 6.166666667 + 76.5625 = 82.729166667
76.5625 + 17.5x + x2 = 82.729166667

Factor a perfect square on the left side:
(x + 8.75)(x + 8.75) = 82.729166667

Calculate the square root of the right side: 9.095557524

Break this problem into two subproblems by setting 
(x + 8.75) equal to 9.095557524 and -9.095557524.

Subproblem 1

x + 8.75 = 9.095557524 Simplifying x + 8.75 = 9.095557524 Reorder the terms: 8.75 + x = 9.095557524 Solving 8.75 + x = 9.095557524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.75' to each side of the equation. 8.75 + -8.75 + x = 9.095557524 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = 9.095557524 + -8.75 x = 9.095557524 + -8.75 Combine like terms: 9.095557524 + -8.75 = 0.345557524 x = 0.345557524 Simplifying x = 0.345557524

Subproblem 2

x + 8.75 = -9.095557524 Simplifying x + 8.75 = -9.095557524 Reorder the terms: 8.75 + x = -9.095557524 Solving 8.75 + x = -9.095557524 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.75' to each side of the equation. 8.75 + -8.75 + x = -9.095557524 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = -9.095557524 + -8.75 x = -9.095557524 + -8.75 Combine like terms: -9.095557524 + -8.75 = -17.845557524 x = -17.845557524 Simplifying x = -17.845557524

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.345557524, -17.845557524}

See similar equations:

| 6n+9n=-3n-21-6 | | 0.7-5=0.6 | | -2k+10=3x+45 | | 4/7*-14-16 | | 6x+40=-4(1-7x) | | 6n+9n=-3n-6 | | 3x-6-4x-4=-7 | | 5+35=-4(7x-10) | | 14/x-5=9-4/x-5 | | -7(k+9)=9(k-5)z | | 60-2/3*12 | | u=3(7n+32)+5(n+1) | | 2y+3y+1=666 | | 5x+(3x-6)= | | -6n+21=12n-115 | | (x+4)(x+4)=96 | | 0.5x=2.1-0.2x | | 6ax-8ay+9bx-12by=0 | | 3x/2-12=3 | | -2(5)-5y=30 | | 95=(2)(A)+(3)(60-A) | | -2(0)-5y=30 | | 3(2y-17)=27 | | -2(-5)-5y=30 | | 1/2×4 | | 6x^2-3x+4=0 | | 1/2(4-k) | | (4x-5)(x^2-6x+4)= | | 3x^2+6=2x | | 8x-2y=4z | | 4-10x=-8 | | 95=2A+3(60-A) |

Equations solver categories