-x^2+75x-2=0

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Solution for -x^2+75x-2=0 equation:


Simplifying
-1x2 + 75x + -2 = 0

Reorder the terms:
-2 + 75x + -1x2 = 0

Solving
-2 + 75x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
2 + -75x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -75x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -75x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -75x + x2 = 0 + -2
-75x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-75x + x2 = -2

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 = -2 + 1406.25

Reorder the terms:
1406.25 + -75x + x2 = -2 + 1406.25

Combine like terms: -2 + 1406.25 = 1404.25
1406.25 + -75x + x2 = 1404.25

Factor a perfect square on the left side:
(x + -37.5)(x + -37.5) = 1404.25

Calculate the square root of the right side: 37.473323845

Break this problem into two subproblems by setting 
(x + -37.5) equal to 37.473323845 and -37.473323845.

Subproblem 1

x + -37.5 = 37.473323845 Simplifying x + -37.5 = 37.473323845 Reorder the terms: -37.5 + x = 37.473323845 Solving -37.5 + x = 37.473323845 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 = 37.473323845 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + x = 37.473323845 + 37.5 x = 37.473323845 + 37.5 Combine like terms: 37.473323845 + 37.5 = 74.973323845 x = 74.973323845 Simplifying x = 74.973323845

Subproblem 2

x + -37.5 = -37.473323845 Simplifying x + -37.5 = -37.473323845 Reorder the terms: -37.5 + x = -37.473323845 Solving -37.5 + x = -37.473323845 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 = -37.473323845 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + x = -37.473323845 + 37.5 x = -37.473323845 + 37.5 Combine like terms: -37.473323845 + 37.5 = 0.026676155 x = 0.026676155 Simplifying x = 0.026676155

Solution

The solution to the problem is based on the solutions from the subproblems. x = {74.973323845, 0.026676155}

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