10x-.83x^2=25

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Solution for 10x-.83x^2=25 equation:


Simplifying
10x + -0.83x2 = 25

Solving
10x + -0.83x2 = 25

Solving for variable 'x'.

Reorder the terms:
-25 + 10x + -0.83x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + 10x + -0.83x2 = 0

Begin completing the square.  Divide all terms by
-0.83 the coefficient of the squared term: 

Divide each side by '-0.83'.
30.12048193 + -12.04819277x + x2 = 0

Move the constant term to the right:

Add '-30.12048193' to each side of the equation.
30.12048193 + -12.04819277x + -30.12048193 + x2 = 0 + -30.12048193

Reorder the terms:
30.12048193 + -30.12048193 + -12.04819277x + x2 = 0 + -30.12048193

Combine like terms: 30.12048193 + -30.12048193 = 0.00000000
0.00000000 + -12.04819277x + x2 = 0 + -30.12048193
-12.04819277x + x2 = 0 + -30.12048193

Combine like terms: 0 + -30.12048193 = -30.12048193
-12.04819277x + x2 = -30.12048193

The x term is -12.04819277x.  Take half its coefficient (-6.024096385).
Square it (36.28973726) and add it to both sides.

Add '36.28973726' to each side of the equation.
-12.04819277x + 36.28973726 + x2 = -30.12048193 + 36.28973726

Reorder the terms:
36.28973726 + -12.04819277x + x2 = -30.12048193 + 36.28973726

Combine like terms: -30.12048193 + 36.28973726 = 6.16925533
36.28973726 + -12.04819277x + x2 = 6.16925533

Factor a perfect square on the left side:
(x + -6.024096385)(x + -6.024096385) = 6.16925533

Calculate the square root of the right side: 2.483798569

Break this problem into two subproblems by setting 
(x + -6.024096385) equal to 2.483798569 and -2.483798569.

Subproblem 1

x + -6.024096385 = 2.483798569 Simplifying x + -6.024096385 = 2.483798569 Reorder the terms: -6.024096385 + x = 2.483798569 Solving -6.024096385 + x = 2.483798569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.024096385' to each side of the equation. -6.024096385 + 6.024096385 + x = 2.483798569 + 6.024096385 Combine like terms: -6.024096385 + 6.024096385 = 0.000000000 0.000000000 + x = 2.483798569 + 6.024096385 x = 2.483798569 + 6.024096385 Combine like terms: 2.483798569 + 6.024096385 = 8.507894954 x = 8.507894954 Simplifying x = 8.507894954

Subproblem 2

x + -6.024096385 = -2.483798569 Simplifying x + -6.024096385 = -2.483798569 Reorder the terms: -6.024096385 + x = -2.483798569 Solving -6.024096385 + x = -2.483798569 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.024096385' to each side of the equation. -6.024096385 + 6.024096385 + x = -2.483798569 + 6.024096385 Combine like terms: -6.024096385 + 6.024096385 = 0.000000000 0.000000000 + x = -2.483798569 + 6.024096385 x = -2.483798569 + 6.024096385 Combine like terms: -2.483798569 + 6.024096385 = 3.540297816 x = 3.540297816 Simplifying x = 3.540297816

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.507894954, 3.540297816}

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