-.054x^2+.39x+1.194=0

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Solution for -.054x^2+.39x+1.194=0 equation:


Simplifying
-0.054x2 + 0.39x + 1.194 = 0

Reorder the terms:
1.194 + 0.39x + -0.054x2 = 0

Solving
1.194 + 0.39x + -0.054x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.054 the coefficient of the squared term: 

Divide each side by '-0.054'.
-22.11111111 + -7.222222222x + x2 = 0

Move the constant term to the right:

Add '22.11111111' to each side of the equation.
-22.11111111 + -7.222222222x + 22.11111111 + x2 = 0 + 22.11111111

Reorder the terms:
-22.11111111 + 22.11111111 + -7.222222222x + x2 = 0 + 22.11111111

Combine like terms: -22.11111111 + 22.11111111 = 0.00000000
0.00000000 + -7.222222222x + x2 = 0 + 22.11111111
-7.222222222x + x2 = 0 + 22.11111111

Combine like terms: 0 + 22.11111111 = 22.11111111
-7.222222222x + x2 = 22.11111111

The x term is -7.222222222x.  Take half its coefficient (-3.611111111).
Square it (13.04012346) and add it to both sides.

Add '13.04012346' to each side of the equation.
-7.222222222x + 13.04012346 + x2 = 22.11111111 + 13.04012346

Reorder the terms:
13.04012346 + -7.222222222x + x2 = 22.11111111 + 13.04012346

Combine like terms: 22.11111111 + 13.04012346 = 35.15123457
13.04012346 + -7.222222222x + x2 = 35.15123457

Factor a perfect square on the left side:
(x + -3.611111111)(x + -3.611111111) = 35.15123457

Calculate the square root of the right side: 5.92884766

Break this problem into two subproblems by setting 
(x + -3.611111111) equal to 5.92884766 and -5.92884766.

Subproblem 1

x + -3.611111111 = 5.92884766 Simplifying x + -3.611111111 = 5.92884766 Reorder the terms: -3.611111111 + x = 5.92884766 Solving -3.611111111 + x = 5.92884766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.611111111' to each side of the equation. -3.611111111 + 3.611111111 + x = 5.92884766 + 3.611111111 Combine like terms: -3.611111111 + 3.611111111 = 0.000000000 0.000000000 + x = 5.92884766 + 3.611111111 x = 5.92884766 + 3.611111111 Combine like terms: 5.92884766 + 3.611111111 = 9.539958771 x = 9.539958771 Simplifying x = 9.539958771

Subproblem 2

x + -3.611111111 = -5.92884766 Simplifying x + -3.611111111 = -5.92884766 Reorder the terms: -3.611111111 + x = -5.92884766 Solving -3.611111111 + x = -5.92884766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.611111111' to each side of the equation. -3.611111111 + 3.611111111 + x = -5.92884766 + 3.611111111 Combine like terms: -3.611111111 + 3.611111111 = 0.000000000 0.000000000 + x = -5.92884766 + 3.611111111 x = -5.92884766 + 3.611111111 Combine like terms: -5.92884766 + 3.611111111 = -2.317736549 x = -2.317736549 Simplifying x = -2.317736549

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.539958771, -2.317736549}

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