x^2+14.6x-2093=0

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Solution for x^2+14.6x-2093=0 equation:


Simplifying
x2 + 14.6x + -2093 = 0

Reorder the terms:
-2093 + 14.6x + x2 = 0

Solving
-2093 + 14.6x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2093' to each side of the equation.
-2093 + 14.6x + 2093 + x2 = 0 + 2093

Reorder the terms:
-2093 + 2093 + 14.6x + x2 = 0 + 2093

Combine like terms: -2093 + 2093 = 0
0 + 14.6x + x2 = 0 + 2093
14.6x + x2 = 0 + 2093

Combine like terms: 0 + 2093 = 2093
14.6x + x2 = 2093

The x term is 14.6x.  Take half its coefficient (7.3).
Square it (53.29) and add it to both sides.

Add '53.29' to each side of the equation.
14.6x + 53.29 + x2 = 2093 + 53.29

Reorder the terms:
53.29 + 14.6x + x2 = 2093 + 53.29

Combine like terms: 2093 + 53.29 = 2146.29
53.29 + 14.6x + x2 = 2146.29

Factor a perfect square on the left side:
(x + 7.3)(x + 7.3) = 2146.29

Calculate the square root of the right side: 46.328069245

Break this problem into two subproblems by setting 
(x + 7.3) equal to 46.328069245 and -46.328069245.

Subproblem 1

x + 7.3 = 46.328069245 Simplifying x + 7.3 = 46.328069245 Reorder the terms: 7.3 + x = 46.328069245 Solving 7.3 + x = 46.328069245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.3' to each side of the equation. 7.3 + -7.3 + x = 46.328069245 + -7.3 Combine like terms: 7.3 + -7.3 = 0.0 0.0 + x = 46.328069245 + -7.3 x = 46.328069245 + -7.3 Combine like terms: 46.328069245 + -7.3 = 39.028069245 x = 39.028069245 Simplifying x = 39.028069245

Subproblem 2

x + 7.3 = -46.328069245 Simplifying x + 7.3 = -46.328069245 Reorder the terms: 7.3 + x = -46.328069245 Solving 7.3 + x = -46.328069245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.3' to each side of the equation. 7.3 + -7.3 + x = -46.328069245 + -7.3 Combine like terms: 7.3 + -7.3 = 0.0 0.0 + x = -46.328069245 + -7.3 x = -46.328069245 + -7.3 Combine like terms: -46.328069245 + -7.3 = -53.628069245 x = -53.628069245 Simplifying x = -53.628069245

Solution

The solution to the problem is based on the solutions from the subproblems. x = {39.028069245, -53.628069245}

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