-0.03*x^2+1.2*x+27.5=0

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Solution for -0.03*x^2+1.2*x+27.5=0 equation:


Simplifying
-0.03x2 + 1.2x + 27.5 = 0

Reorder the terms:
27.5 + 1.2x + -0.03x2 = 0

Solving
27.5 + 1.2x + -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'.
-916.6666667 + -40x + x2 = 0

Move the constant term to the right:

Add '916.6666667' to each side of the equation.
-916.6666667 + -40x + 916.6666667 + x2 = 0 + 916.6666667

Reorder the terms:
-916.6666667 + 916.6666667 + -40x + x2 = 0 + 916.6666667

Combine like terms: -916.6666667 + 916.6666667 = 0.0000000
0.0000000 + -40x + x2 = 0 + 916.6666667
-40x + x2 = 0 + 916.6666667

Combine like terms: 0 + 916.6666667 = 916.6666667
-40x + x2 = 916.6666667

The x term is -40x.  Take half its coefficient (-20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
-40x + 400 + x2 = 916.6666667 + 400

Reorder the terms:
400 + -40x + x2 = 916.6666667 + 400

Combine like terms: 916.6666667 + 400 = 1316.6666667
400 + -40x + x2 = 1316.6666667

Factor a perfect square on the left side:
(x + -20)(x + -20) = 1316.6666667

Calculate the square root of the right side: 36.285901762

Break this problem into two subproblems by setting 
(x + -20) equal to 36.285901762 and -36.285901762.

Subproblem 1

x + -20 = 36.285901762 Simplifying x + -20 = 36.285901762 Reorder the terms: -20 + x = 36.285901762 Solving -20 + x = 36.285901762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 36.285901762 + 20 Combine like terms: -20 + 20 = 0 0 + x = 36.285901762 + 20 x = 36.285901762 + 20 Combine like terms: 36.285901762 + 20 = 56.285901762 x = 56.285901762 Simplifying x = 56.285901762

Subproblem 2

x + -20 = -36.285901762 Simplifying x + -20 = -36.285901762 Reorder the terms: -20 + x = -36.285901762 Solving -20 + x = -36.285901762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -36.285901762 + 20 Combine like terms: -20 + 20 = 0 0 + x = -36.285901762 + 20 x = -36.285901762 + 20 Combine like terms: -36.285901762 + 20 = -16.285901762 x = -16.285901762 Simplifying x = -16.285901762

Solution

The solution to the problem is based on the solutions from the subproblems. x = {56.285901762, -16.285901762}

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