x^2+9x=-7

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Solution for x^2+9x=-7 equation:


Simplifying
x2 + 9x = -7

Reorder the terms:
9x + x2 = -7

Solving
9x + x2 = -7

Solving for variable 'x'.

Reorder the terms:
7 + 9x + x2 = -7 + 7

Combine like terms: -7 + 7 = 0
7 + 9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 9x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + 9x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 9x + x2 = 0 + -7
9x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
9x + x2 = -7

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 = -7 + 20.25

Reorder the terms:
20.25 + 9x + x2 = -7 + 20.25

Combine like terms: -7 + 20.25 = 13.25
20.25 + 9x + x2 = 13.25

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(x + 4.5) equal to 3.640054945 and -3.640054945.

Subproblem 1

x + 4.5 = 3.640054945 Simplifying x + 4.5 = 3.640054945 Reorder the terms: 4.5 + x = 3.640054945 Solving 4.5 + x = 3.640054945 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 = 3.640054945 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 3.640054945 + -4.5 x = 3.640054945 + -4.5 Combine like terms: 3.640054945 + -4.5 = -0.859945055 x = -0.859945055 Simplifying x = -0.859945055

Subproblem 2

x + 4.5 = -3.640054945 Simplifying x + 4.5 = -3.640054945 Reorder the terms: 4.5 + x = -3.640054945 Solving 4.5 + x = -3.640054945 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 = -3.640054945 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -3.640054945 + -4.5 x = -3.640054945 + -4.5 Combine like terms: -3.640054945 + -4.5 = -8.140054945 x = -8.140054945 Simplifying x = -8.140054945

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.859945055, -8.140054945}

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