5x^2+2-12=42-37x

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Solution for 5x^2+2-12=42-37x equation:


Simplifying
5x2 + 2 + -12 = 42 + -37x

Reorder the terms:
2 + -12 + 5x2 = 42 + -37x

Combine like terms: 2 + -12 = -10
-10 + 5x2 = 42 + -37x

Solving
-10 + 5x2 = 42 + -37x

Solving for variable 'x'.

Reorder the terms:
-10 + -42 + 37x + 5x2 = 42 + -37x + -42 + 37x

Combine like terms: -10 + -42 = -52
-52 + 37x + 5x2 = 42 + -37x + -42 + 37x

Reorder the terms:
-52 + 37x + 5x2 = 42 + -42 + -37x + 37x

Combine like terms: 42 + -42 = 0
-52 + 37x + 5x2 = 0 + -37x + 37x
-52 + 37x + 5x2 = -37x + 37x

Combine like terms: -37x + 37x = 0
-52 + 37x + 5x2 = 0

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

Divide each side by '5'.
-10.4 + 7.4x + x2 = 0

Move the constant term to the right:

Add '10.4' to each side of the equation.
-10.4 + 7.4x + 10.4 + x2 = 0 + 10.4

Reorder the terms:
-10.4 + 10.4 + 7.4x + x2 = 0 + 10.4

Combine like terms: -10.4 + 10.4 = 0.0
0.0 + 7.4x + x2 = 0 + 10.4
7.4x + x2 = 0 + 10.4

Combine like terms: 0 + 10.4 = 10.4
7.4x + x2 = 10.4

The x term is 7.4x.  Take half its coefficient (3.7).
Square it (13.69) and add it to both sides.

Add '13.69' to each side of the equation.
7.4x + 13.69 + x2 = 10.4 + 13.69

Reorder the terms:
13.69 + 7.4x + x2 = 10.4 + 13.69

Combine like terms: 10.4 + 13.69 = 24.09
13.69 + 7.4x + x2 = 24.09

Factor a perfect square on the left side:
(x + 3.7)(x + 3.7) = 24.09

Calculate the square root of the right side: 4.908156477

Break this problem into two subproblems by setting 
(x + 3.7) equal to 4.908156477 and -4.908156477.

Subproblem 1

x + 3.7 = 4.908156477 Simplifying x + 3.7 = 4.908156477 Reorder the terms: 3.7 + x = 4.908156477 Solving 3.7 + x = 4.908156477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.7' to each side of the equation. 3.7 + -3.7 + x = 4.908156477 + -3.7 Combine like terms: 3.7 + -3.7 = 0.0 0.0 + x = 4.908156477 + -3.7 x = 4.908156477 + -3.7 Combine like terms: 4.908156477 + -3.7 = 1.208156477 x = 1.208156477 Simplifying x = 1.208156477

Subproblem 2

x + 3.7 = -4.908156477 Simplifying x + 3.7 = -4.908156477 Reorder the terms: 3.7 + x = -4.908156477 Solving 3.7 + x = -4.908156477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.7' to each side of the equation. 3.7 + -3.7 + x = -4.908156477 + -3.7 Combine like terms: 3.7 + -3.7 = 0.0 0.0 + x = -4.908156477 + -3.7 x = -4.908156477 + -3.7 Combine like terms: -4.908156477 + -3.7 = -8.608156477 x = -8.608156477 Simplifying x = -8.608156477

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.208156477, -8.608156477}

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