-x^2-x+900=0

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Solution for -x^2-x+900=0 equation:


Simplifying
-1x2 + -1x + 900 = 0

Reorder the terms:
900 + -1x + -1x2 = 0

Solving
900 + -1x + -1x2 = 0

Solving for variable 'x'.

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

Divide each side by '-1'.
-900 + x + x2 = 0

Move the constant term to the right:

Add '900' to each side of the equation.
-900 + x + 900 + x2 = 0 + 900

Reorder the terms:
-900 + 900 + x + x2 = 0 + 900

Combine like terms: -900 + 900 = 0
0 + x + x2 = 0 + 900
x + x2 = 0 + 900

Combine like terms: 0 + 900 = 900
x + x2 = 900

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 900 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 900 + 0.25

Combine like terms: 900 + 0.25 = 900.25
1.25 + x2 = 900.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 900.25

Calculate the square root of the right side: 30.004166377

Break this problem into two subproblems by setting 
(x + 0.5) equal to 30.004166377 and -30.004166377.

Subproblem 1

x + 0.5 = 30.004166377 Simplifying x + 0.5 = 30.004166377 Reorder the terms: 0.5 + x = 30.004166377 Solving 0.5 + x = 30.004166377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 30.004166377 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 30.004166377 + -0.5 x = 30.004166377 + -0.5 Combine like terms: 30.004166377 + -0.5 = 29.504166377 x = 29.504166377 Simplifying x = 29.504166377

Subproblem 2

x + 0.5 = -30.004166377 Simplifying x + 0.5 = -30.004166377 Reorder the terms: 0.5 + x = -30.004166377 Solving 0.5 + x = -30.004166377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -30.004166377 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -30.004166377 + -0.5 x = -30.004166377 + -0.5 Combine like terms: -30.004166377 + -0.5 = -30.504166377 x = -30.504166377 Simplifying x = -30.504166377

Solution

The solution to the problem is based on the solutions from the subproblems. x = {29.504166377, -30.504166377}

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