-0.03x^2+2.1x+5.4=0

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Solution for -0.03x^2+2.1x+5.4=0 equation:


Simplifying
-0.03x2 + 2.1x + 5.4 = 0

Reorder the terms:
5.4 + 2.1x + -0.03x2 = 0

Solving
5.4 + 2.1x + -0.03x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.03 the coefficient of the squared term: 

Divide each side by '-0.03'.
-180 + -70x + x2 = 0

Move the constant term to the right:

Add '180' to each side of the equation.
-180 + -70x + 180 + x2 = 0 + 180

Reorder the terms:
-180 + 180 + -70x + x2 = 0 + 180

Combine like terms: -180 + 180 = 0
0 + -70x + x2 = 0 + 180
-70x + x2 = 0 + 180

Combine like terms: 0 + 180 = 180
-70x + x2 = 180

The x term is -70x.  Take half its coefficient (-35).
Square it (1225) and add it to both sides.

Add '1225' to each side of the equation.
-70x + 1225 + x2 = 180 + 1225

Reorder the terms:
1225 + -70x + x2 = 180 + 1225

Combine like terms: 180 + 1225 = 1405
1225 + -70x + x2 = 1405

Factor a perfect square on the left side:
(x + -35)(x + -35) = 1405

Calculate the square root of the right side: 37.483329628

Break this problem into two subproblems by setting 
(x + -35) equal to 37.483329628 and -37.483329628.

Subproblem 1

x + -35 = 37.483329628 Simplifying x + -35 = 37.483329628 Reorder the terms: -35 + x = 37.483329628 Solving -35 + x = 37.483329628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + x = 37.483329628 + 35 Combine like terms: -35 + 35 = 0 0 + x = 37.483329628 + 35 x = 37.483329628 + 35 Combine like terms: 37.483329628 + 35 = 72.483329628 x = 72.483329628 Simplifying x = 72.483329628

Subproblem 2

x + -35 = -37.483329628 Simplifying x + -35 = -37.483329628 Reorder the terms: -35 + x = -37.483329628 Solving -35 + x = -37.483329628 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + x = -37.483329628 + 35 Combine like terms: -35 + 35 = 0 0 + x = -37.483329628 + 35 x = -37.483329628 + 35 Combine like terms: -37.483329628 + 35 = -2.483329628 x = -2.483329628 Simplifying x = -2.483329628

Solution

The solution to the problem is based on the solutions from the subproblems. x = {72.483329628, -2.483329628}

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