5x^2-18x-4=0

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Solution for 5x^2-18x-4=0 equation:


Simplifying
5x2 + -18x + -4 = 0

Reorder the terms:
-4 + -18x + 5x2 = 0

Solving
-4 + -18x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-0.8 + -3.6x + x2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + -3.6x + 0.8 + x2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + -3.6x + x2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + -3.6x + x2 = 0 + 0.8
-3.6x + x2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
-3.6x + x2 = 0.8

The x term is -3.6x.  Take half its coefficient (-1.8).
Square it (3.24) and add it to both sides.

Add '3.24' to each side of the equation.
-3.6x + 3.24 + x2 = 0.8 + 3.24

Reorder the terms:
3.24 + -3.6x + x2 = 0.8 + 3.24

Combine like terms: 0.8 + 3.24 = 4.04
3.24 + -3.6x + x2 = 4.04

Factor a perfect square on the left side:
(x + -1.8)(x + -1.8) = 4.04

Calculate the square root of the right side: 2.009975124

Break this problem into two subproblems by setting 
(x + -1.8) equal to 2.009975124 and -2.009975124.

Subproblem 1

x + -1.8 = 2.009975124 Simplifying x + -1.8 = 2.009975124 Reorder the terms: -1.8 + x = 2.009975124 Solving -1.8 + x = 2.009975124 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = 2.009975124 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = 2.009975124 + 1.8 x = 2.009975124 + 1.8 Combine like terms: 2.009975124 + 1.8 = 3.809975124 x = 3.809975124 Simplifying x = 3.809975124

Subproblem 2

x + -1.8 = -2.009975124 Simplifying x + -1.8 = -2.009975124 Reorder the terms: -1.8 + x = -2.009975124 Solving -1.8 + x = -2.009975124 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + x = -2.009975124 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + x = -2.009975124 + 1.8 x = -2.009975124 + 1.8 Combine like terms: -2.009975124 + 1.8 = -0.209975124 x = -0.209975124 Simplifying x = -0.209975124

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.809975124, -0.209975124}

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