x^2-75x-60=0

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Solution for x^2-75x-60=0 equation:


Simplifying
x2 + -75x + -60 = 0

Reorder the terms:
-60 + -75x + x2 = 0

Solving
-60 + -75x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + -75x + 60 + x2 = 0 + 60

Reorder the terms:
-60 + 60 + -75x + x2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + -75x + x2 = 0 + 60
-75x + x2 = 0 + 60

Combine like terms: 0 + 60 = 60
-75x + x2 = 60

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 = 60 + 1406.25

Reorder the terms:
1406.25 + -75x + x2 = 60 + 1406.25

Combine like terms: 60 + 1406.25 = 1466.25
1406.25 + -75x + x2 = 1466.25

Factor a perfect square on the left side:
(x + -37.5)(x + -37.5) = 1466.25

Calculate the square root of the right side: 38.291643997

Break this problem into two subproblems by setting 
(x + -37.5) equal to 38.291643997 and -38.291643997.

Subproblem 1

x + -37.5 = 38.291643997 Simplifying x + -37.5 = 38.291643997 Reorder the terms: -37.5 + x = 38.291643997 Solving -37.5 + x = 38.291643997 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 = 38.291643997 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + x = 38.291643997 + 37.5 x = 38.291643997 + 37.5 Combine like terms: 38.291643997 + 37.5 = 75.791643997 x = 75.791643997 Simplifying x = 75.791643997

Subproblem 2

x + -37.5 = -38.291643997 Simplifying x + -37.5 = -38.291643997 Reorder the terms: -37.5 + x = -38.291643997 Solving -37.5 + x = -38.291643997 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 = -38.291643997 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + x = -38.291643997 + 37.5 x = -38.291643997 + 37.5 Combine like terms: -38.291643997 + 37.5 = -0.791643997 x = -0.791643997 Simplifying x = -0.791643997

Solution

The solution to the problem is based on the solutions from the subproblems. x = {75.791643997, -0.791643997}

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