0.4x^2-30x+125=0

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Solution for 0.4x^2-30x+125=0 equation:


Simplifying
0.4x2 + -30x + 125 = 0

Reorder the terms:
125 + -30x + 0.4x2 = 0

Solving
125 + -30x + 0.4x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.4'.
312.5 + -75x + x2 = 0

Move the constant term to the right:

Add '-312.5' to each side of the equation.
312.5 + -75x + -312.5 + x2 = 0 + -312.5

Reorder the terms:
312.5 + -312.5 + -75x + x2 = 0 + -312.5

Combine like terms: 312.5 + -312.5 = 0.0
0.0 + -75x + x2 = 0 + -312.5
-75x + x2 = 0 + -312.5

Combine like terms: 0 + -312.5 = -312.5
-75x + x2 = -312.5

The x term is -75x.  Take half its coefficient (-37.5).
Square it (1406.25) and add it to both sides.

Add '1406.25' to each side of the equation.
-75x + 1406.25 + x2 = -312.5 + 1406.25

Reorder the terms:
1406.25 + -75x + x2 = -312.5 + 1406.25

Combine like terms: -312.5 + 1406.25 = 1093.75
1406.25 + -75x + x2 = 1093.75

Factor a perfect square on the left side:
(x + -37.5)(x + -37.5) = 1093.75

Calculate the square root of the right side: 33.071891388

Break this problem into two subproblems by setting 
(x + -37.5) equal to 33.071891388 and -33.071891388.

Subproblem 1

x + -37.5 = 33.071891388 Simplifying x + -37.5 = 33.071891388 Reorder the terms: -37.5 + x = 33.071891388 Solving -37.5 + x = 33.071891388 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '37.5' to each side of the equation. -37.5 + 37.5 + x = 33.071891388 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + x = 33.071891388 + 37.5 x = 33.071891388 + 37.5 Combine like terms: 33.071891388 + 37.5 = 70.571891388 x = 70.571891388 Simplifying x = 70.571891388

Subproblem 2

x + -37.5 = -33.071891388 Simplifying x + -37.5 = -33.071891388 Reorder the terms: -37.5 + x = -33.071891388 Solving -37.5 + x = -33.071891388 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '37.5' to each side of the equation. -37.5 + 37.5 + x = -33.071891388 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + x = -33.071891388 + 37.5 x = -33.071891388 + 37.5 Combine like terms: -33.071891388 + 37.5 = 4.428108612 x = 4.428108612 Simplifying x = 4.428108612

Solution

The solution to the problem is based on the solutions from the subproblems. x = {70.571891388, 4.428108612}

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