0=61.35x-x^2-58.014

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Solution for 0=61.35x-x^2-58.014 equation:


Simplifying
0 = 61.35x + -1x2 + -58.014

Reorder the terms:
0 = -58.014 + 61.35x + -1x2

Solving
0 = -58.014 + 61.35x + -1x2

Solving for variable 'x'.

Combine like terms: 0 + 58.014 = 58.014
58.014 + -61.35x + x2 = -58.014 + 61.35x + -1x2 + 58.014 + -61.35x + x2

Reorder the terms:
58.014 + -61.35x + x2 = -58.014 + 58.014 + 61.35x + -61.35x + -1x2 + x2

Combine like terms: -58.014 + 58.014 = 0.000
58.014 + -61.35x + x2 = 0.000 + 61.35x + -61.35x + -1x2 + x2
58.014 + -61.35x + x2 = 61.35x + -61.35x + -1x2 + x2

Combine like terms: 61.35x + -61.35x = 0.00
58.014 + -61.35x + x2 = 0.00 + -1x2 + x2
58.014 + -61.35x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
58.014 + -61.35x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-58.014' to each side of the equation.
58.014 + -61.35x + -58.014 + x2 = 0 + -58.014

Reorder the terms:
58.014 + -58.014 + -61.35x + x2 = 0 + -58.014

Combine like terms: 58.014 + -58.014 = 0.000
0.000 + -61.35x + x2 = 0 + -58.014
-61.35x + x2 = 0 + -58.014

Combine like terms: 0 + -58.014 = -58.014
-61.35x + x2 = -58.014

The x term is -61.35x.  Take half its coefficient (-30.675).
Square it (940.955625) and add it to both sides.

Add '940.955625' to each side of the equation.
-61.35x + 940.955625 + x2 = -58.014 + 940.955625

Reorder the terms:
940.955625 + -61.35x + x2 = -58.014 + 940.955625

Combine like terms: -58.014 + 940.955625 = 882.941625
940.955625 + -61.35x + x2 = 882.941625

Factor a perfect square on the left side:
(x + -30.675)(x + -30.675) = 882.941625

Calculate the square root of the right side: 29.714333662

Break this problem into two subproblems by setting 
(x + -30.675) equal to 29.714333662 and -29.714333662.

Subproblem 1

x + -30.675 = 29.714333662 Simplifying x + -30.675 = 29.714333662 Reorder the terms: -30.675 + x = 29.714333662 Solving -30.675 + x = 29.714333662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30.675' to each side of the equation. -30.675 + 30.675 + x = 29.714333662 + 30.675 Combine like terms: -30.675 + 30.675 = 0.000 0.000 + x = 29.714333662 + 30.675 x = 29.714333662 + 30.675 Combine like terms: 29.714333662 + 30.675 = 60.389333662 x = 60.389333662 Simplifying x = 60.389333662

Subproblem 2

x + -30.675 = -29.714333662 Simplifying x + -30.675 = -29.714333662 Reorder the terms: -30.675 + x = -29.714333662 Solving -30.675 + x = -29.714333662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30.675' to each side of the equation. -30.675 + 30.675 + x = -29.714333662 + 30.675 Combine like terms: -30.675 + 30.675 = 0.000 0.000 + x = -29.714333662 + 30.675 x = -29.714333662 + 30.675 Combine like terms: -29.714333662 + 30.675 = 0.960666338 x = 0.960666338 Simplifying x = 0.960666338

Solution

The solution to the problem is based on the solutions from the subproblems. x = {60.389333662, 0.960666338}

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