15x^2+100x-25=0

Simple and best practice solution for 15x^2+100x-25=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 15x^2+100x-25=0 equation: 


Simplifying
15x2 + 100x + -25 = 0

Reorder the terms:
-25 + 100x + 15x2 = 0

Solving
-25 + 100x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-5 + 20x + 3x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-5 + 20x + 3x2)' equal to zero and attempt to solve:

Simplifying
-5 + 20x + 3x2 = 0

Solving
-5 + 20x + 3x2 = 0

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

Divide each side by '3'.
-1.666666667 + 6.666666667x + x2 = 0

Move the constant term to the right:

Add '1.666666667' to each side of the equation.
-1.666666667 + 6.666666667x + 1.666666667 + x2 = 0 + 1.666666667

Reorder the terms:
-1.666666667 + 1.666666667 + 6.666666667x + x2 = 0 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + 6.666666667x + x2 = 0 + 1.666666667
6.666666667x + x2 = 0 + 1.666666667

Combine like terms: 0 + 1.666666667 = 1.666666667
6.666666667x + x2 = 1.666666667

The x term is 6.666666667x.  Take half its coefficient (3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
6.666666667x + 11.11111112 + x2 = 1.666666667 + 11.11111112

Reorder the terms:
11.11111112 + 6.666666667x + x2 = 1.666666667 + 11.11111112

Combine like terms: 1.666666667 + 11.11111112 = 12.777777787
11.11111112 + 6.666666667x + x2 = 12.777777787

Factor a perfect square on the left side:
(x + 3.333333334)(x + 3.333333334) = 12.777777787

Calculate the square root of the right side: 3.574601766

Break this problem into two subproblems by setting 
(x + 3.333333334) equal to 3.574601766 and -3.574601766.


Subproblem 1
x + 3.333333334 = 3.574601766

Simplifying
x + 3.333333334 = 3.574601766

Reorder the terms:
3.333333334 + x = 3.574601766

Solving
3.333333334 + x = 3.574601766

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = 3.574601766 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = 3.574601766 + -3.333333334
x = 3.574601766 + -3.333333334

Combine like terms: 3.574601766 + -3.333333334 = 0.241268432
x = 0.241268432

Simplifying
x = 0.241268432


Subproblem 2
x + 3.333333334 = -3.574601766

Simplifying
x + 3.333333334 = -3.574601766

Reorder the terms:
3.333333334 + x = -3.574601766

Solving
3.333333334 + x = -3.574601766

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = -3.574601766 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = -3.574601766 + -3.333333334
x = -3.574601766 + -3.333333334

Combine like terms: -3.574601766 + -3.333333334 = -6.9079351
x = -6.9079351

Simplifying
x = -6.9079351


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.241268432, -6.9079351}
Solution
x = {0.241268432, -6.9079351}

See similar equations:

| m^2+100=0 | | 7-20-o^2=0 | | 2y+4=5y-14 | | 5m^20-5m^18=0 | | 3x^2+6x=105 | | 2p-7p=30 | | -6+8v=v^2 | | 9.60x+.5(8-x)=.10(103) | | c^2+6x=-3 | | 3+p= | | 3x^2-22-16= | | 0.40x+.05(16-x)=.10(36) | | 12-2m+5=m | | -6+5=n | | -6-5=n | | 12-18=m | | 56+-6x= | | 3t^2=5t-1 | | Graphy=x+3 | | 8x-(5x-4)= | | 16x(x+2)-8=16x+24 | | -3-8-4x-7x=-2-8 | | 0.3333(y-6)=4y-0.4(2-y) | | -2(9-3a)-(5a+2)=-25 | | 4z^2-117=3 | | .01*.3= | | 10k-[3k+(-3+5k)]= | | 12x-7x-10=0 | | T^2+12T+42=0 | | 7-8x=-21 | | s^2-45+8=0 | | 4(3x-2)=12 |

Equations solver categories