x*x=-9x-5

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Solution for x*x=-9x-5 equation:


Simplifying
x * x = -9x + -5

Multiply x * x
x2 = -9x + -5

Reorder the terms:
x2 = -5 + -9x

Solving
x2 = -5 + -9x

Solving for variable 'x'.

Reorder the terms:
5 + 9x + x2 = -5 + -9x + 5 + 9x

Reorder the terms:
5 + 9x + x2 = -5 + 5 + -9x + 9x

Combine like terms: -5 + 5 = 0
5 + 9x + x2 = 0 + -9x + 9x
5 + 9x + x2 = -9x + 9x

Combine like terms: -9x + 9x = 0
5 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 9x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 9x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 9x + x2 = 0 + -5
9x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
9x + x2 = -5

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = -5 + 20.25

Reorder the terms:
20.25 + 9x + x2 = -5 + 20.25

Combine like terms: -5 + 20.25 = 15.25
20.25 + 9x + x2 = 15.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(x + 4.5) equal to 3.905124838 and -3.905124838.

Subproblem 1

x + 4.5 = 3.905124838 Simplifying x + 4.5 = 3.905124838 Reorder the terms: 4.5 + x = 3.905124838 Solving 4.5 + x = 3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 3.905124838 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 3.905124838 + -4.5 x = 3.905124838 + -4.5 Combine like terms: 3.905124838 + -4.5 = -0.594875162 x = -0.594875162 Simplifying x = -0.594875162

Subproblem 2

x + 4.5 = -3.905124838 Simplifying x + 4.5 = -3.905124838 Reorder the terms: 4.5 + x = -3.905124838 Solving 4.5 + x = -3.905124838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -3.905124838 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -3.905124838 + -4.5 x = -3.905124838 + -4.5 Combine like terms: -3.905124838 + -4.5 = -8.405124838 x = -8.405124838 Simplifying x = -8.405124838

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.594875162, -8.405124838}

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