3.09x(x-6.91)=24.95

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Solution for 3.09x(x-6.91)=24.95 equation: 


Simplifying
3.09x(x + -6.91) = 24.95

Reorder the terms:
3.09x(-6.91 + x) = 24.95
(-6.91 * 3.09x + x * 3.09x) = 24.95
(-21.3519x + 3.09x2) = 24.95

Solving
-21.3519x + 3.09x2 = 24.95

Solving for variable 'x'.

Reorder the terms:
-24.95 + -21.3519x + 3.09x2 = 24.95 + -24.95

Combine like terms: 24.95 + -24.95 = 0.00
-24.95 + -21.3519x + 3.09x2 = 0.00

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

Divide each side by '3.09'.
-8.074433657 + -6.91x + x2 = 0

Move the constant term to the right:

Add '8.074433657' to each side of the equation.
-8.074433657 + -6.91x + 8.074433657 + x2 = 0 + 8.074433657

Reorder the terms:
-8.074433657 + 8.074433657 + -6.91x + x2 = 0 + 8.074433657

Combine like terms: -8.074433657 + 8.074433657 = 0.000000000
0.000000000 + -6.91x + x2 = 0 + 8.074433657
-6.91x + x2 = 0 + 8.074433657

Combine like terms: 0 + 8.074433657 = 8.074433657
-6.91x + x2 = 8.074433657

The x term is -6.91x.  Take half its coefficient (-3.455).
Square it (11.937025) and add it to both sides.

Add '11.937025' to each side of the equation.
-6.91x + 11.937025 + x2 = 8.074433657 + 11.937025

Reorder the terms:
11.937025 + -6.91x + x2 = 8.074433657 + 11.937025

Combine like terms: 8.074433657 + 11.937025 = 20.011458657
11.937025 + -6.91x + x2 = 20.011458657

Factor a perfect square on the left side:
(x + -3.455)(x + -3.455) = 20.011458657

Calculate the square root of the right side: 4.473416888

Break this problem into two subproblems by setting 
(x + -3.455) equal to 4.473416888 and -4.473416888.


Subproblem 1
x + -3.455 = 4.473416888

Simplifying
x + -3.455 = 4.473416888

Reorder the terms:
-3.455 + x = 4.473416888

Solving
-3.455 + x = 4.473416888

Solving for variable 'x'.

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

Add '3.455' to each side of the equation.
-3.455 + 3.455 + x = 4.473416888 + 3.455

Combine like terms: -3.455 + 3.455 = 0.000
0.000 + x = 4.473416888 + 3.455
x = 4.473416888 + 3.455

Combine like terms: 4.473416888 + 3.455 = 7.928416888
x = 7.928416888

Simplifying
x = 7.928416888


Subproblem 2
x + -3.455 = -4.473416888

Simplifying
x + -3.455 = -4.473416888

Reorder the terms:
-3.455 + x = -4.473416888

Solving
-3.455 + x = -4.473416888

Solving for variable 'x'.

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

Add '3.455' to each side of the equation.
-3.455 + 3.455 + x = -4.473416888 + 3.455

Combine like terms: -3.455 + 3.455 = 0.000
0.000 + x = -4.473416888 + 3.455
x = -4.473416888 + 3.455

Combine like terms: -4.473416888 + 3.455 = -1.018416888
x = -1.018416888

Simplifying
x = -1.018416888


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.928416888, -1.018416888}

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