125.54-148.152x+20.3556x^2=0

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Solution for 125.54-148.152x+20.3556x^2=0 equation:


Simplifying
125.54 + -148.152x + 20.3556x2 = 0

Solving
125.54 + -148.152x + 20.3556x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
20.3556 the coefficient of the squared term: 

Divide each side by '20.3556'.
6.167344613 + -7.278193716x + x2 = 0

Move the constant term to the right:

Add '-6.167344613' to each side of the equation.
6.167344613 + -7.278193716x + -6.167344613 + x2 = 0 + -6.167344613

Reorder the terms:
6.167344613 + -6.167344613 + -7.278193716x + x2 = 0 + -6.167344613

Combine like terms: 6.167344613 + -6.167344613 = 0.000000000
0.000000000 + -7.278193716x + x2 = 0 + -6.167344613
-7.278193716x + x2 = 0 + -6.167344613

Combine like terms: 0 + -6.167344613 = -6.167344613
-7.278193716x + x2 = -6.167344613

The x term is -7.278193716x.  Take half its coefficient (-3.639096858).
Square it (13.24302594) and add it to both sides.

Add '13.24302594' to each side of the equation.
-7.278193716x + 13.24302594 + x2 = -6.167344613 + 13.24302594

Reorder the terms:
13.24302594 + -7.278193716x + x2 = -6.167344613 + 13.24302594

Combine like terms: -6.167344613 + 13.24302594 = 7.075681327
13.24302594 + -7.278193716x + x2 = 7.075681327

Factor a perfect square on the left side:
(x + -3.639096858)(x + -3.639096858) = 7.075681327

Calculate the square root of the right side: 2.660015287

Break this problem into two subproblems by setting 
(x + -3.639096858) equal to 2.660015287 and -2.660015287.

Subproblem 1

x + -3.639096858 = 2.660015287 Simplifying x + -3.639096858 = 2.660015287 Reorder the terms: -3.639096858 + x = 2.660015287 Solving -3.639096858 + x = 2.660015287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.639096858' to each side of the equation. -3.639096858 + 3.639096858 + x = 2.660015287 + 3.639096858 Combine like terms: -3.639096858 + 3.639096858 = 0.000000000 0.000000000 + x = 2.660015287 + 3.639096858 x = 2.660015287 + 3.639096858 Combine like terms: 2.660015287 + 3.639096858 = 6.299112145 x = 6.299112145 Simplifying x = 6.299112145

Subproblem 2

x + -3.639096858 = -2.660015287 Simplifying x + -3.639096858 = -2.660015287 Reorder the terms: -3.639096858 + x = -2.660015287 Solving -3.639096858 + x = -2.660015287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.639096858' to each side of the equation. -3.639096858 + 3.639096858 + x = -2.660015287 + 3.639096858 Combine like terms: -3.639096858 + 3.639096858 = 0.000000000 0.000000000 + x = -2.660015287 + 3.639096858 x = -2.660015287 + 3.639096858 Combine like terms: -2.660015287 + 3.639096858 = 0.979081571 x = 0.979081571 Simplifying x = 0.979081571

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.299112145, 0.979081571}

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