5x(x+3)+4=9-(x+1)

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Solution for 5x(x+3)+4=9-(x+1) equation:


Simplifying
5x(x + 3) + 4 = 9 + -1(x + 1)

Reorder the terms:
5x(3 + x) + 4 = 9 + -1(x + 1)
(3 * 5x + x * 5x) + 4 = 9 + -1(x + 1)
(15x + 5x2) + 4 = 9 + -1(x + 1)

Reorder the terms:
4 + 15x + 5x2 = 9 + -1(x + 1)

Reorder the terms:
4 + 15x + 5x2 = 9 + -1(1 + x)
4 + 15x + 5x2 = 9 + (1 * -1 + x * -1)
4 + 15x + 5x2 = 9 + (-1 + -1x)

Combine like terms: 9 + -1 = 8
4 + 15x + 5x2 = 8 + -1x

Solving
4 + 15x + 5x2 = 8 + -1x

Solving for variable 'x'.

Reorder the terms:
4 + -8 + 15x + x + 5x2 = 8 + -1x + -8 + x

Combine like terms: 4 + -8 = -4
-4 + 15x + x + 5x2 = 8 + -1x + -8 + x

Combine like terms: 15x + x = 16x
-4 + 16x + 5x2 = 8 + -1x + -8 + x

Reorder the terms:
-4 + 16x + 5x2 = 8 + -8 + -1x + x

Combine like terms: 8 + -8 = 0
-4 + 16x + 5x2 = 0 + -1x + x
-4 + 16x + 5x2 = -1x + x

Combine like terms: -1x + x = 0
-4 + 16x + 5x2 = 0

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

Divide each side by '5'.
-0.8 + 3.2x + x2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + 3.2x + 0.8 + x2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + 3.2x + x2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + 3.2x + x2 = 0 + 0.8
3.2x + x2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
3.2x + x2 = 0.8

The x term is 3.2x.  Take half its coefficient (1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
3.2x + 2.56 + x2 = 0.8 + 2.56

Reorder the terms:
2.56 + 3.2x + x2 = 0.8 + 2.56

Combine like terms: 0.8 + 2.56 = 3.36
2.56 + 3.2x + x2 = 3.36

Factor a perfect square on the left side:
(x + 1.6)(x + 1.6) = 3.36

Calculate the square root of the right side: 1.833030278

Break this problem into two subproblems by setting 
(x + 1.6) equal to 1.833030278 and -1.833030278.

Subproblem 1

x + 1.6 = 1.833030278 Simplifying x + 1.6 = 1.833030278 Reorder the terms: 1.6 + x = 1.833030278 Solving 1.6 + x = 1.833030278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = 1.833030278 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = 1.833030278 + -1.6 x = 1.833030278 + -1.6 Combine like terms: 1.833030278 + -1.6 = 0.233030278 x = 0.233030278 Simplifying x = 0.233030278

Subproblem 2

x + 1.6 = -1.833030278 Simplifying x + 1.6 = -1.833030278 Reorder the terms: 1.6 + x = -1.833030278 Solving 1.6 + x = -1.833030278 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.6' to each side of the equation. 1.6 + -1.6 + x = -1.833030278 + -1.6 Combine like terms: 1.6 + -1.6 = 0.0 0.0 + x = -1.833030278 + -1.6 x = -1.833030278 + -1.6 Combine like terms: -1.833030278 + -1.6 = -3.433030278 x = -3.433030278 Simplifying x = -3.433030278

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.233030278, -3.433030278}

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