6x^2+25x-75=0

Simple and best practice solution for 6x^2+25x-75=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 6x^2+25x-75=0 equation: 


Simplifying
6x2 + 25x + -75 = 0

Reorder the terms:
-75 + 25x + 6x2 = 0

Solving
-75 + 25x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-12.5 + 4.166666667x + x2 = 0

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + 4.166666667x + 12.5 + x2 = 0 + 12.5

Reorder the terms:
-12.5 + 12.5 + 4.166666667x + x2 = 0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + 4.166666667x + x2 = 0 + 12.5
4.166666667x + x2 = 0 + 12.5

Combine like terms: 0 + 12.5 = 12.5
4.166666667x + x2 = 12.5

The x term is 4.166666667x.  Take half its coefficient (2.083333334).
Square it (4.340277781) and add it to both sides.

Add '4.340277781' to each side of the equation.
4.166666667x + 4.340277781 + x2 = 12.5 + 4.340277781

Reorder the terms:
4.340277781 + 4.166666667x + x2 = 12.5 + 4.340277781

Combine like terms: 12.5 + 4.340277781 = 16.840277781
4.340277781 + 4.166666667x + x2 = 16.840277781

Factor a perfect square on the left side:
(x + 2.083333334)(x + 2.083333334) = 16.840277781

Calculate the square root of the right side: 4.103690751

Break this problem into two subproblems by setting 
(x + 2.083333334) equal to 4.103690751 and -4.103690751.


Subproblem 1
x + 2.083333334 = 4.103690751

Simplifying
x + 2.083333334 = 4.103690751

Reorder the terms:
2.083333334 + x = 4.103690751

Solving
2.083333334 + x = 4.103690751

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.083333334' to each side of the equation.
2.083333334 + -2.083333334 + x = 4.103690751 + -2.083333334

Combine like terms: 2.083333334 + -2.083333334 = 0.000000000
0.000000000 + x = 4.103690751 + -2.083333334
x = 4.103690751 + -2.083333334

Combine like terms: 4.103690751 + -2.083333334 = 2.020357417
x = 2.020357417

Simplifying
x = 2.020357417


Subproblem 2
x + 2.083333334 = -4.103690751

Simplifying
x + 2.083333334 = -4.103690751

Reorder the terms:
2.083333334 + x = -4.103690751

Solving
2.083333334 + x = -4.103690751

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.083333334' to each side of the equation.
2.083333334 + -2.083333334 + x = -4.103690751 + -2.083333334

Combine like terms: 2.083333334 + -2.083333334 = 0.000000000
0.000000000 + x = -4.103690751 + -2.083333334
x = -4.103690751 + -2.083333334

Combine like terms: -4.103690751 + -2.083333334 = -6.187024085
x = -6.187024085

Simplifying
x = -6.187024085


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.020357417, -6.187024085}

See similar equations:

| -5x+1+6=-13 | | Y-325=25(x-10) | | 3(7x+5)=5(4x+8)-21 | | 18w+6m= | | ln(x)=-100 | | 0.5x^2=2+3sin(t) | | -17r+8=-315 | | 10m+32= | | 2-4x^2=3x | | 12t+1(1-7t)=31 | | S-1.5(16)=6.2 | | 4r^2-7r+3=0 | | 3+3v=39 | | S-1.5x=6.2 | | (-3-2i)(4+2i)= | | 8x+x=-45 | | 0.59x=6-0.41x | | 75=3(-6x-5)-1 | | X-8+3=-2 | | 2(y-3)=2x+6 | | 2x^2-8=20 | | -1-5a=99 | | 3(3x-8)=2(4x-6)+2 | | 4(3y+2+10)= | | 0.42+0.39n=0.0885 | | 2x+7+4x=4x+16+x | | 6(2x-3)-3x=2x-18+x | | 15x=14x-5 | | 4-3r=46 | | 3n(n+9+2n)= | | 7h+18-h+12=-54 | | -5-q=0 |

Equations solver categories