3x^2+30x-100=0

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Solution for 3x^2+30x-100=0 equation:


Simplifying
3x2 + 30x + -100 = 0

Reorder the terms:
-100 + 30x + 3x2 = 0

Solving
-100 + 30x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-33.33333333 + 10x + x2 = 0

Move the constant term to the right:

Add '33.33333333' to each side of the equation.
-33.33333333 + 10x + 33.33333333 + x2 = 0 + 33.33333333

Reorder the terms:
-33.33333333 + 33.33333333 + 10x + x2 = 0 + 33.33333333

Combine like terms: -33.33333333 + 33.33333333 = 0.00000000
0.00000000 + 10x + x2 = 0 + 33.33333333
10x + x2 = 0 + 33.33333333

Combine like terms: 0 + 33.33333333 = 33.33333333
10x + x2 = 33.33333333

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 33.33333333 + 25

Reorder the terms:
25 + 10x + x2 = 33.33333333 + 25

Combine like terms: 33.33333333 + 25 = 58.33333333
25 + 10x + x2 = 58.33333333

Factor a perfect square on the left side:
(x + 5)(x + 5) = 58.33333333

Calculate the square root of the right side: 7.637626158

Break this problem into two subproblems by setting 
(x + 5) equal to 7.637626158 and -7.637626158.

Subproblem 1

x + 5 = 7.637626158 Simplifying x + 5 = 7.637626158 Reorder the terms: 5 + x = 7.637626158 Solving 5 + x = 7.637626158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 7.637626158 + -5 Combine like terms: 5 + -5 = 0 0 + x = 7.637626158 + -5 x = 7.637626158 + -5 Combine like terms: 7.637626158 + -5 = 2.637626158 x = 2.637626158 Simplifying x = 2.637626158

Subproblem 2

x + 5 = -7.637626158 Simplifying x + 5 = -7.637626158 Reorder the terms: 5 + x = -7.637626158 Solving 5 + x = -7.637626158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -7.637626158 + -5 Combine like terms: 5 + -5 = 0 0 + x = -7.637626158 + -5 x = -7.637626158 + -5 Combine like terms: -7.637626158 + -5 = -12.637626158 x = -12.637626158 Simplifying x = -12.637626158

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.637626158, -12.637626158}

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