x*(x+5)=-3

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Solution for x*(x+5)=-3 equation:


Simplifying
x(x + 5) = -3

Reorder the terms:
x(5 + x) = -3
(5 * x + x * x) = -3
(5x + x2) = -3

Solving
5x + x2 = -3

Solving for variable 'x'.

Reorder the terms:
3 + 5x + x2 = -3 + 3

Combine like terms: -3 + 3 = 0
3 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 5x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + 5x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5x + x2 = 0 + -3
5x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
5x + x2 = -3

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -3 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -3 + 6.25

Combine like terms: -3 + 6.25 = 3.25
6.25 + 5x + x2 = 3.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + 2.5) equal to 1.802775638 and -1.802775638.

Subproblem 1

x + 2.5 = 1.802775638 Simplifying x + 2.5 = 1.802775638 Reorder the terms: 2.5 + x = 1.802775638 Solving 2.5 + x = 1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 1.802775638 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 1.802775638 + -2.5 x = 1.802775638 + -2.5 Combine like terms: 1.802775638 + -2.5 = -0.697224362 x = -0.697224362 Simplifying x = -0.697224362

Subproblem 2

x + 2.5 = -1.802775638 Simplifying x + 2.5 = -1.802775638 Reorder the terms: 2.5 + x = -1.802775638 Solving 2.5 + x = -1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -1.802775638 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -1.802775638 + -2.5 x = -1.802775638 + -2.5 Combine like terms: -1.802775638 + -2.5 = -4.302775638 x = -4.302775638 Simplifying x = -4.302775638

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.697224362, -4.302775638}

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