x^2+5x^2-25x-125=0

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Solution for x^2+5x^2-25x-125=0 equation:


Simplifying
x2 + 5x2 + -25x + -125 = 0

Reorder the terms:
-125 + -25x + x2 + 5x2 = 0

Combine like terms: x2 + 5x2 = 6x2
-125 + -25x + 6x2 = 0

Solving
-125 + -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'.
-20.83333333 + -4.166666667x + x2 = 0

Move the constant term to the right:

Add '20.83333333' to each side of the equation.
-20.83333333 + -4.166666667x + 20.83333333 + x2 = 0 + 20.83333333

Reorder the terms:
-20.83333333 + 20.83333333 + -4.166666667x + x2 = 0 + 20.83333333

Combine like terms: -20.83333333 + 20.83333333 = 0.00000000
0.00000000 + -4.166666667x + x2 = 0 + 20.83333333
-4.166666667x + x2 = 0 + 20.83333333

Combine like terms: 0 + 20.83333333 = 20.83333333
-4.166666667x + x2 = 20.83333333

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 = 20.83333333 + 4.340277781

Reorder the terms:
4.340277781 + -4.166666667x + x2 = 20.83333333 + 4.340277781

Combine like terms: 20.83333333 + 4.340277781 = 25.173611111
4.340277781 + -4.166666667x + x2 = 25.173611111

Factor a perfect square on the left side:
(x + -2.083333334)(x + -2.083333334) = 25.173611111

Calculate the square root of the right side: 5.017331074

Break this problem into two subproblems by setting 
(x + -2.083333334) equal to 5.017331074 and -5.017331074.

Subproblem 1

x + -2.083333334 = 5.017331074 Simplifying x + -2.083333334 = 5.017331074 Reorder the terms: -2.083333334 + x = 5.017331074 Solving -2.083333334 + x = 5.017331074 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 = 5.017331074 + 2.083333334 Combine like terms: -2.083333334 + 2.083333334 = 0.000000000 0.000000000 + x = 5.017331074 + 2.083333334 x = 5.017331074 + 2.083333334 Combine like terms: 5.017331074 + 2.083333334 = 7.100664408 x = 7.100664408 Simplifying x = 7.100664408

Subproblem 2

x + -2.083333334 = -5.017331074 Simplifying x + -2.083333334 = -5.017331074 Reorder the terms: -2.083333334 + x = -5.017331074 Solving -2.083333334 + x = -5.017331074 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 = -5.017331074 + 2.083333334 Combine like terms: -2.083333334 + 2.083333334 = 0.000000000 0.000000000 + x = -5.017331074 + 2.083333334 x = -5.017331074 + 2.083333334 Combine like terms: -5.017331074 + 2.083333334 = -2.93399774 x = -2.93399774 Simplifying x = -2.93399774

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.100664408, -2.93399774}

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