0=x^2+53x-730

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Solution for 0=x^2+53x-730 equation:


Simplifying
0 = x2 + 53x + -730

Reorder the terms:
0 = -730 + 53x + x2

Solving
0 = -730 + 53x + x2

Solving for variable 'x'.

Combine like terms: 0 + 730 = 730
730 + -53x + -1x2 = -730 + 53x + x2 + 730 + -53x + -1x2

Reorder the terms:
730 + -53x + -1x2 = -730 + 730 + 53x + -53x + x2 + -1x2

Combine like terms: -730 + 730 = 0
730 + -53x + -1x2 = 0 + 53x + -53x + x2 + -1x2
730 + -53x + -1x2 = 53x + -53x + x2 + -1x2

Combine like terms: 53x + -53x = 0
730 + -53x + -1x2 = 0 + x2 + -1x2
730 + -53x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
730 + -53x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-730 + 53x + x2 = 0

Move the constant term to the right:

Add '730' to each side of the equation.
-730 + 53x + 730 + x2 = 0 + 730

Reorder the terms:
-730 + 730 + 53x + x2 = 0 + 730

Combine like terms: -730 + 730 = 0
0 + 53x + x2 = 0 + 730
53x + x2 = 0 + 730

Combine like terms: 0 + 730 = 730
53x + x2 = 730

The x term is 53x.  Take half its coefficient (26.5).
Square it (702.25) and add it to both sides.

Add '702.25' to each side of the equation.
53x + 702.25 + x2 = 730 + 702.25

Reorder the terms:
702.25 + 53x + x2 = 730 + 702.25

Combine like terms: 730 + 702.25 = 1432.25
702.25 + 53x + x2 = 1432.25

Factor a perfect square on the left side:
(x + 26.5)(x + 26.5) = 1432.25

Calculate the square root of the right side: 37.84507894

Break this problem into two subproblems by setting 
(x + 26.5) equal to 37.84507894 and -37.84507894.

Subproblem 1

x + 26.5 = 37.84507894 Simplifying x + 26.5 = 37.84507894 Reorder the terms: 26.5 + x = 37.84507894 Solving 26.5 + x = 37.84507894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-26.5' to each side of the equation. 26.5 + -26.5 + x = 37.84507894 + -26.5 Combine like terms: 26.5 + -26.5 = 0.0 0.0 + x = 37.84507894 + -26.5 x = 37.84507894 + -26.5 Combine like terms: 37.84507894 + -26.5 = 11.34507894 x = 11.34507894 Simplifying x = 11.34507894

Subproblem 2

x + 26.5 = -37.84507894 Simplifying x + 26.5 = -37.84507894 Reorder the terms: 26.5 + x = -37.84507894 Solving 26.5 + x = -37.84507894 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-26.5' to each side of the equation. 26.5 + -26.5 + x = -37.84507894 + -26.5 Combine like terms: 26.5 + -26.5 = 0.0 0.0 + x = -37.84507894 + -26.5 x = -37.84507894 + -26.5 Combine like terms: -37.84507894 + -26.5 = -64.34507894 x = -64.34507894 Simplifying x = -64.34507894

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.34507894, -64.34507894}

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