-9x^2+10x+25=0

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Solution for -9x^2+10x+25=0 equation:


Simplifying
-9x2 + 10x + 25 = 0

Reorder the terms:
25 + 10x + -9x2 = 0

Solving
25 + 10x + -9x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
-2.777777778 + -1.111111111x + x2 = 0

Move the constant term to the right:

Add '2.777777778' to each side of the equation.
-2.777777778 + -1.111111111x + 2.777777778 + x2 = 0 + 2.777777778

Reorder the terms:
-2.777777778 + 2.777777778 + -1.111111111x + x2 = 0 + 2.777777778

Combine like terms: -2.777777778 + 2.777777778 = 0.000000000
0.000000000 + -1.111111111x + x2 = 0 + 2.777777778
-1.111111111x + x2 = 0 + 2.777777778

Combine like terms: 0 + 2.777777778 = 2.777777778
-1.111111111x + x2 = 2.777777778

The x term is -1.111111111x.  Take half its coefficient (-0.5555555555).
Square it (0.3086419752) and add it to both sides.

Add '0.3086419752' to each side of the equation.
-1.111111111x + 0.3086419752 + x2 = 2.777777778 + 0.3086419752

Reorder the terms:
0.3086419752 + -1.111111111x + x2 = 2.777777778 + 0.3086419752

Combine like terms: 2.777777778 + 0.3086419752 = 3.0864197532
0.3086419752 + -1.111111111x + x2 = 3.0864197532

Factor a perfect square on the left side:
(x + -0.5555555555)(x + -0.5555555555) = 3.0864197532

Calculate the square root of the right side: 1.756820922

Break this problem into two subproblems by setting 
(x + -0.5555555555) equal to 1.756820922 and -1.756820922.

Subproblem 1

x + -0.5555555555 = 1.756820922 Simplifying x + -0.5555555555 = 1.756820922 Reorder the terms: -0.5555555555 + x = 1.756820922 Solving -0.5555555555 + x = 1.756820922 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5555555555' to each side of the equation. -0.5555555555 + 0.5555555555 + x = 1.756820922 + 0.5555555555 Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000 0.0000000000 + x = 1.756820922 + 0.5555555555 x = 1.756820922 + 0.5555555555 Combine like terms: 1.756820922 + 0.5555555555 = 2.3123764775 x = 2.3123764775 Simplifying x = 2.3123764775

Subproblem 2

x + -0.5555555555 = -1.756820922 Simplifying x + -0.5555555555 = -1.756820922 Reorder the terms: -0.5555555555 + x = -1.756820922 Solving -0.5555555555 + x = -1.756820922 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5555555555' to each side of the equation. -0.5555555555 + 0.5555555555 + x = -1.756820922 + 0.5555555555 Combine like terms: -0.5555555555 + 0.5555555555 = 0.0000000000 0.0000000000 + x = -1.756820922 + 0.5555555555 x = -1.756820922 + 0.5555555555 Combine like terms: -1.756820922 + 0.5555555555 = -1.2012653665 x = -1.2012653665 Simplifying x = -1.2012653665

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.3123764775, -1.2012653665}

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