x^2+75x+3=0

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Solution for x^2+75x+3=0 equation:


Simplifying
x2 + 75x + 3 = 0

Reorder the terms:
3 + 75x + x2 = 0

Solving
3 + 75x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 75x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 75x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 75x + x2 = 0 + -3
75x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
75x + x2 = -3

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 = -3 + 1406.25

Reorder the terms:
1406.25 + 75x + x2 = -3 + 1406.25

Combine like terms: -3 + 1406.25 = 1403.25
1406.25 + 75x + x2 = 1403.25

Factor a perfect square on the left side:
(x + 37.5)(x + 37.5) = 1403.25

Calculate the square root of the right side: 37.459978644

Break this problem into two subproblems by setting 
(x + 37.5) equal to 37.459978644 and -37.459978644.

Subproblem 1

x + 37.5 = 37.459978644 Simplifying x + 37.5 = 37.459978644 Reorder the terms: 37.5 + x = 37.459978644 Solving 37.5 + x = 37.459978644 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 = 37.459978644 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + x = 37.459978644 + -37.5 x = 37.459978644 + -37.5 Combine like terms: 37.459978644 + -37.5 = -0.040021356 x = -0.040021356 Simplifying x = -0.040021356

Subproblem 2

x + 37.5 = -37.459978644 Simplifying x + 37.5 = -37.459978644 Reorder the terms: 37.5 + x = -37.459978644 Solving 37.5 + x = -37.459978644 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 = -37.459978644 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + x = -37.459978644 + -37.5 x = -37.459978644 + -37.5 Combine like terms: -37.459978644 + -37.5 = -74.959978644 x = -74.959978644 Simplifying x = -74.959978644

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.040021356, -74.959978644}

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