x^2+1.80x-18.29=0

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Solution for x^2+1.80x-18.29=0 equation:


Simplifying
x2 + 1.80x + -18.29 = 0

Reorder the terms:
-18.29 + 1.80x + x2 = 0

Solving
-18.29 + 1.80x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '18.29' to each side of the equation.
-18.29 + 1.80x + 18.29 + x2 = 0 + 18.29

Reorder the terms:
-18.29 + 18.29 + 1.80x + x2 = 0 + 18.29

Combine like terms: -18.29 + 18.29 = 0.00
0.00 + 1.80x + x2 = 0 + 18.29
1.80x + x2 = 0 + 18.29

Combine like terms: 0 + 18.29 = 18.29
1.80x + x2 = 18.29

The x term is 1.80x.  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.
1.80x + 0.81 + x2 = 18.29 + 0.81

Reorder the terms:
0.81 + 1.80x + x2 = 18.29 + 0.81

Combine like terms: 18.29 + 0.81 = 19.1
0.81 + 1.80x + x2 = 19.1

Factor a perfect square on the left side:
(x + 0.9)(x + 0.9) = 19.1

Calculate the square root of the right side: 4.370354677

Break this problem into two subproblems by setting 
(x + 0.9) equal to 4.370354677 and -4.370354677.

Subproblem 1

x + 0.9 = 4.370354677 Simplifying x + 0.9 = 4.370354677 Reorder the terms: 0.9 + x = 4.370354677 Solving 0.9 + x = 4.370354677 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 = 4.370354677 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 4.370354677 + -0.9 x = 4.370354677 + -0.9 Combine like terms: 4.370354677 + -0.9 = 3.470354677 x = 3.470354677 Simplifying x = 3.470354677

Subproblem 2

x + 0.9 = -4.370354677 Simplifying x + 0.9 = -4.370354677 Reorder the terms: 0.9 + x = -4.370354677 Solving 0.9 + x = -4.370354677 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 = -4.370354677 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -4.370354677 + -0.9 x = -4.370354677 + -0.9 Combine like terms: -4.370354677 + -0.9 = -5.270354677 x = -5.270354677 Simplifying x = -5.270354677

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.470354677, -5.270354677}

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