(x+5)+(x+8)+(3x-3)+(x^2-3)=58

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Solution for (x+5)+(x+8)+(3x-3)+(x^2-3)=58 equation:


Simplifying
(x + 5) + (x + 8) + (3x + -3) + (x2 + -3) = 58

Reorder the terms:
(5 + x) + (x + 8) + (3x + -3) + (x2 + -3) = 58

Remove parenthesis around (5 + x)
5 + x + (x + 8) + (3x + -3) + (x2 + -3) = 58

Reorder the terms:
5 + x + (8 + x) + (3x + -3) + (x2 + -3) = 58

Remove parenthesis around (8 + x)
5 + x + 8 + x + (3x + -3) + (x2 + -3) = 58

Reorder the terms:
5 + x + 8 + x + (-3 + 3x) + (x2 + -3) = 58

Remove parenthesis around (-3 + 3x)
5 + x + 8 + x + -3 + 3x + (x2 + -3) = 58

Reorder the terms:
5 + x + 8 + x + -3 + 3x + (-3 + x2) = 58

Remove parenthesis around (-3 + x2)
5 + x + 8 + x + -3 + 3x + -3 + x2 = 58

Reorder the terms:
5 + 8 + -3 + -3 + x + x + 3x + x2 = 58

Combine like terms: 5 + 8 = 13
13 + -3 + -3 + x + x + 3x + x2 = 58

Combine like terms: 13 + -3 = 10
10 + -3 + x + x + 3x + x2 = 58

Combine like terms: 10 + -3 = 7
7 + x + x + 3x + x2 = 58

Combine like terms: x + x = 2x
7 + 2x + 3x + x2 = 58

Combine like terms: 2x + 3x = 5x
7 + 5x + x2 = 58

Solving
7 + 5x + x2 = 58

Solving for variable 'x'.

Reorder the terms:
7 + -58 + 5x + x2 = 58 + -58

Combine like terms: 7 + -58 = -51
-51 + 5x + x2 = 58 + -58

Combine like terms: 58 + -58 = 0
-51 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '51' to each side of the equation.
-51 + 5x + 51 + x2 = 0 + 51

Reorder the terms:
-51 + 51 + 5x + x2 = 0 + 51

Combine like terms: -51 + 51 = 0
0 + 5x + x2 = 0 + 51
5x + x2 = 0 + 51

Combine like terms: 0 + 51 = 51
5x + x2 = 51

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 = 51 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 51 + 6.25

Combine like terms: 51 + 6.25 = 57.25
6.25 + 5x + x2 = 57.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 57.25

Calculate the square root of the right side: 7.566372975

Break this problem into two subproblems by setting 
(x + 2.5) equal to 7.566372975 and -7.566372975.

Subproblem 1

x + 2.5 = 7.566372975 Simplifying x + 2.5 = 7.566372975 Reorder the terms: 2.5 + x = 7.566372975 Solving 2.5 + x = 7.566372975 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 = 7.566372975 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 7.566372975 + -2.5 x = 7.566372975 + -2.5 Combine like terms: 7.566372975 + -2.5 = 5.066372975 x = 5.066372975 Simplifying x = 5.066372975

Subproblem 2

x + 2.5 = -7.566372975 Simplifying x + 2.5 = -7.566372975 Reorder the terms: 2.5 + x = -7.566372975 Solving 2.5 + x = -7.566372975 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 = -7.566372975 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -7.566372975 + -2.5 x = -7.566372975 + -2.5 Combine like terms: -7.566372975 + -2.5 = -10.066372975 x = -10.066372975 Simplifying x = -10.066372975

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.066372975, -10.066372975}

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