5x(x+3)+7x=-7

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Solution for 5x(x+3)+7x=-7 equation:


Simplifying
5x(x + 3) + 7x = -7

Reorder the terms:
5x(3 + x) + 7x = -7
(3 * 5x + x * 5x) + 7x = -7
(15x + 5x2) + 7x = -7

Reorder the terms:
15x + 7x + 5x2 = -7

Combine like terms: 15x + 7x = 22x
22x + 5x2 = -7

Solving
22x + 5x2 = -7

Solving for variable 'x'.

Reorder the terms:
7 + 22x + 5x2 = -7 + 7

Combine like terms: -7 + 7 = 0
7 + 22x + 5x2 = 0

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

Divide each side by '5'.
1.4 + 4.4x + x2 = 0

Move the constant term to the right:

Add '-1.4' to each side of the equation.
1.4 + 4.4x + -1.4 + x2 = 0 + -1.4

Reorder the terms:
1.4 + -1.4 + 4.4x + x2 = 0 + -1.4

Combine like terms: 1.4 + -1.4 = 0.0
0.0 + 4.4x + x2 = 0 + -1.4
4.4x + x2 = 0 + -1.4

Combine like terms: 0 + -1.4 = -1.4
4.4x + x2 = -1.4

The x term is 4.4x.  Take half its coefficient (2.2).
Square it (4.84) and add it to both sides.

Add '4.84' to each side of the equation.
4.4x + 4.84 + x2 = -1.4 + 4.84

Reorder the terms:
4.84 + 4.4x + x2 = -1.4 + 4.84

Combine like terms: -1.4 + 4.84 = 3.44
4.84 + 4.4x + x2 = 3.44

Factor a perfect square on the left side:
(x + 2.2)(x + 2.2) = 3.44

Calculate the square root of the right side: 1.854723699

Break this problem into two subproblems by setting 
(x + 2.2) equal to 1.854723699 and -1.854723699.

Subproblem 1

x + 2.2 = 1.854723699 Simplifying x + 2.2 = 1.854723699 Reorder the terms: 2.2 + x = 1.854723699 Solving 2.2 + x = 1.854723699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.2' to each side of the equation. 2.2 + -2.2 + x = 1.854723699 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + x = 1.854723699 + -2.2 x = 1.854723699 + -2.2 Combine like terms: 1.854723699 + -2.2 = -0.345276301 x = -0.345276301 Simplifying x = -0.345276301

Subproblem 2

x + 2.2 = -1.854723699 Simplifying x + 2.2 = -1.854723699 Reorder the terms: 2.2 + x = -1.854723699 Solving 2.2 + x = -1.854723699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.2' to each side of the equation. 2.2 + -2.2 + x = -1.854723699 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + x = -1.854723699 + -2.2 x = -1.854723699 + -2.2 Combine like terms: -1.854723699 + -2.2 = -4.054723699 x = -4.054723699 Simplifying x = -4.054723699

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.345276301, -4.054723699}

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