0.065x(x+1940)+0.05=970

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Solution for 0.065x(x+1940)+0.05=970 equation:


Simplifying
0.065x(x + 1940) + 0.05 = 970

Reorder the terms:
0.065x(1940 + x) + 0.05 = 970
(1940 * 0.065x + x * 0.065x) + 0.05 = 970
(126.1x + 0.065x2) + 0.05 = 970

Reorder the terms:
0.05 + 126.1x + 0.065x2 = 970

Solving
0.05 + 126.1x + 0.065x2 = 970

Solving for variable 'x'.

Reorder the terms:
0.05 + -970 + 126.1x + 0.065x2 = 970 + -970

Combine like terms: 0.05 + -970 = -969.95
-969.95 + 126.1x + 0.065x2 = 970 + -970

Combine like terms: 970 + -970 = 0
-969.95 + 126.1x + 0.065x2 = 0

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

Divide each side by '0.065'.
-14922.30769 + 1940x + x2 = 0

Move the constant term to the right:

Add '14922.30769' to each side of the equation.
-14922.30769 + 1940x + 14922.30769 + x2 = 0 + 14922.30769

Reorder the terms:
-14922.30769 + 14922.30769 + 1940x + x2 = 0 + 14922.30769

Combine like terms: -14922.30769 + 14922.30769 = 0.00000
0.00000 + 1940x + x2 = 0 + 14922.30769
1940x + x2 = 0 + 14922.30769

Combine like terms: 0 + 14922.30769 = 14922.30769
1940x + x2 = 14922.30769

The x term is 1940x.  Take half its coefficient (970).
Square it (940900) and add it to both sides.

Add '940900' to each side of the equation.
1940x + 940900 + x2 = 14922.30769 + 940900

Reorder the terms:
940900 + 1940x + x2 = 14922.30769 + 940900

Combine like terms: 14922.30769 + 940900 = 955822.30769
940900 + 1940x + x2 = 955822.30769

Factor a perfect square on the left side:
(x + 970)(x + 970) = 955822.30769

Calculate the square root of the right side: 977.661652971

Break this problem into two subproblems by setting 
(x + 970) equal to 977.661652971 and -977.661652971.

Subproblem 1

x + 970 = 977.661652971 Simplifying x + 970 = 977.661652971 Reorder the terms: 970 + x = 977.661652971 Solving 970 + x = 977.661652971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-970' to each side of the equation. 970 + -970 + x = 977.661652971 + -970 Combine like terms: 970 + -970 = 0 0 + x = 977.661652971 + -970 x = 977.661652971 + -970 Combine like terms: 977.661652971 + -970 = 7.661652971 x = 7.661652971 Simplifying x = 7.661652971

Subproblem 2

x + 970 = -977.661652971 Simplifying x + 970 = -977.661652971 Reorder the terms: 970 + x = -977.661652971 Solving 970 + x = -977.661652971 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-970' to each side of the equation. 970 + -970 + x = -977.661652971 + -970 Combine like terms: 970 + -970 = 0 0 + x = -977.661652971 + -970 x = -977.661652971 + -970 Combine like terms: -977.661652971 + -970 = -1947.661652971 x = -1947.661652971 Simplifying x = -1947.661652971

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.661652971, -1947.661652971}

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