5x^2-18+4=12x+39

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Solution for 5x^2-18+4=12x+39 equation:


Simplifying
5x2 + -18 + 4 = 12x + 39

Reorder the terms:
-18 + 4 + 5x2 = 12x + 39

Combine like terms: -18 + 4 = -14
-14 + 5x2 = 12x + 39

Reorder the terms:
-14 + 5x2 = 39 + 12x

Solving
-14 + 5x2 = 39 + 12x

Solving for variable 'x'.

Reorder the terms:
-14 + -39 + -12x + 5x2 = 39 + 12x + -39 + -12x

Combine like terms: -14 + -39 = -53
-53 + -12x + 5x2 = 39 + 12x + -39 + -12x

Reorder the terms:
-53 + -12x + 5x2 = 39 + -39 + 12x + -12x

Combine like terms: 39 + -39 = 0
-53 + -12x + 5x2 = 0 + 12x + -12x
-53 + -12x + 5x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-53 + -12x + 5x2 = 0

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

Divide each side by '5'.
-10.6 + -2.4x + x2 = 0

Move the constant term to the right:

Add '10.6' to each side of the equation.
-10.6 + -2.4x + 10.6 + x2 = 0 + 10.6

Reorder the terms:
-10.6 + 10.6 + -2.4x + x2 = 0 + 10.6

Combine like terms: -10.6 + 10.6 = 0.0
0.0 + -2.4x + x2 = 0 + 10.6
-2.4x + x2 = 0 + 10.6

Combine like terms: 0 + 10.6 = 10.6
-2.4x + x2 = 10.6

The x term is -2.4x.  Take half its coefficient (-1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
-2.4x + 1.44 + x2 = 10.6 + 1.44

Reorder the terms:
1.44 + -2.4x + x2 = 10.6 + 1.44

Combine like terms: 10.6 + 1.44 = 12.04
1.44 + -2.4x + x2 = 12.04

Factor a perfect square on the left side:
(x + -1.2)(x + -1.2) = 12.04

Calculate the square root of the right side: 3.469870315

Break this problem into two subproblems by setting 
(x + -1.2) equal to 3.469870315 and -3.469870315.

Subproblem 1

x + -1.2 = 3.469870315 Simplifying x + -1.2 = 3.469870315 Reorder the terms: -1.2 + x = 3.469870315 Solving -1.2 + x = 3.469870315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 3.469870315 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 3.469870315 + 1.2 x = 3.469870315 + 1.2 Combine like terms: 3.469870315 + 1.2 = 4.669870315 x = 4.669870315 Simplifying x = 4.669870315

Subproblem 2

x + -1.2 = -3.469870315 Simplifying x + -1.2 = -3.469870315 Reorder the terms: -1.2 + x = -3.469870315 Solving -1.2 + x = -3.469870315 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -3.469870315 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -3.469870315 + 1.2 x = -3.469870315 + 1.2 Combine like terms: -3.469870315 + 1.2 = -2.269870315 x = -2.269870315 Simplifying x = -2.269870315

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.669870315, -2.269870315}

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