541.2-57.5x+1.25x^2=0

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Solution for 541.2-57.5x+1.25x^2=0 equation:


Simplifying
541.2 + -57.5x + 1.25x2 = 0

Solving
541.2 + -57.5x + 1.25x2 = 0

Solving for variable 'x'.

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

Divide each side by '1.25'.
432.96 + -46x + x2 = 0

Move the constant term to the right:

Add '-432.96' to each side of the equation.
432.96 + -46x + -432.96 + x2 = 0 + -432.96

Reorder the terms:
432.96 + -432.96 + -46x + x2 = 0 + -432.96

Combine like terms: 432.96 + -432.96 = 0.00
0.00 + -46x + x2 = 0 + -432.96
-46x + x2 = 0 + -432.96

Combine like terms: 0 + -432.96 = -432.96
-46x + x2 = -432.96

The x term is -46x.  Take half its coefficient (-23).
Square it (529) and add it to both sides.

Add '529' to each side of the equation.
-46x + 529 + x2 = -432.96 + 529

Reorder the terms:
529 + -46x + x2 = -432.96 + 529

Combine like terms: -432.96 + 529 = 96.04
529 + -46x + x2 = 96.04

Factor a perfect square on the left side:
(x + -23)(x + -23) = 96.04

Calculate the square root of the right side: 9.8

Break this problem into two subproblems by setting 
(x + -23) equal to 9.8 and -9.8.

Subproblem 1

x + -23 = 9.8 Simplifying x + -23 = 9.8 Reorder the terms: -23 + x = 9.8 Solving -23 + x = 9.8 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + x = 9.8 + 23 Combine like terms: -23 + 23 = 0 0 + x = 9.8 + 23 x = 9.8 + 23 Combine like terms: 9.8 + 23 = 32.8 x = 32.8 Simplifying x = 32.8

Subproblem 2

x + -23 = -9.8 Simplifying x + -23 = -9.8 Reorder the terms: -23 + x = -9.8 Solving -23 + x = -9.8 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + x = -9.8 + 23 Combine like terms: -23 + 23 = 0 0 + x = -9.8 + 23 x = -9.8 + 23 Combine like terms: -9.8 + 23 = 13.2 x = 13.2 Simplifying x = 13.2

Solution

The solution to the problem is based on the solutions from the subproblems. x = {32.8, 13.2}

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