x^2+1.8x-0.1152=0

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Solution for x^2+1.8x-0.1152=0 equation:


Simplifying
x2 + 1.8x + -0.1152 = 0

Reorder the terms:
-0.1152 + 1.8x + x2 = 0

Solving
-0.1152 + 1.8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.1152' to each side of the equation.
-0.1152 + 1.8x + 0.1152 + x2 = 0 + 0.1152

Reorder the terms:
-0.1152 + 0.1152 + 1.8x + x2 = 0 + 0.1152

Combine like terms: -0.1152 + 0.1152 = 0.0000
0.0000 + 1.8x + x2 = 0 + 0.1152
1.8x + x2 = 0 + 0.1152

Combine like terms: 0 + 0.1152 = 0.1152
1.8x + x2 = 0.1152

The x term is 1.8x.  Take half its coefficient (0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
1.8x + 0.81 + x2 = 0.1152 + 0.81

Reorder the terms:
0.81 + 1.8x + x2 = 0.1152 + 0.81

Combine like terms: 0.1152 + 0.81 = 0.9252
0.81 + 1.8x + x2 = 0.9252

Factor a perfect square on the left side:
(x + 0.9)(x + 0.9) = 0.9252

Calculate the square root of the right side: 0.961873173

Break this problem into two subproblems by setting 
(x + 0.9) equal to 0.961873173 and -0.961873173.

Subproblem 1

x + 0.9 = 0.961873173 Simplifying x + 0.9 = 0.961873173 Reorder the terms: 0.9 + x = 0.961873173 Solving 0.9 + x = 0.961873173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = 0.961873173 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 0.961873173 + -0.9 x = 0.961873173 + -0.9 Combine like terms: 0.961873173 + -0.9 = 0.061873173 x = 0.061873173 Simplifying x = 0.061873173

Subproblem 2

x + 0.9 = -0.961873173 Simplifying x + 0.9 = -0.961873173 Reorder the terms: 0.9 + x = -0.961873173 Solving 0.9 + x = -0.961873173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = -0.961873173 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -0.961873173 + -0.9 x = -0.961873173 + -0.9 Combine like terms: -0.961873173 + -0.9 = -1.861873173 x = -1.861873173 Simplifying x = -1.861873173

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.061873173, -1.861873173}

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