20x-.83x^2=25

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Solution for 20x-.83x^2=25 equation:


Simplifying
20x + -0.83x2 = 25

Solving
20x + -0.83x2 = 25

Solving for variable 'x'.

Reorder the terms:
-25 + 20x + -0.83x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + 20x + -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 + -24.09638554x + x2 = 0

Move the constant term to the right:

Add '-30.12048193' to each side of the equation.
30.12048193 + -24.09638554x + -30.12048193 + x2 = 0 + -30.12048193

Reorder the terms:
30.12048193 + -30.12048193 + -24.09638554x + x2 = 0 + -30.12048193

Combine like terms: 30.12048193 + -30.12048193 = 0.00000000
0.00000000 + -24.09638554x + x2 = 0 + -30.12048193
-24.09638554x + x2 = 0 + -30.12048193

Combine like terms: 0 + -30.12048193 = -30.12048193
-24.09638554x + x2 = -30.12048193

The x term is -24.09638554x.  Take half its coefficient (-12.04819277).
Square it (145.1589490) and add it to both sides.

Add '145.1589490' to each side of the equation.
-24.09638554x + 145.1589490 + x2 = -30.12048193 + 145.1589490

Reorder the terms:
145.1589490 + -24.09638554x + x2 = -30.12048193 + 145.1589490

Combine like terms: -30.12048193 + 145.1589490 = 115.03846707
145.1589490 + -24.09638554x + x2 = 115.03846707

Factor a perfect square on the left side:
(x + -12.04819277)(x + -12.04819277) = 115.03846707

Calculate the square root of the right side: 10.725598681

Break this problem into two subproblems by setting 
(x + -12.04819277) equal to 10.725598681 and -10.725598681.

Subproblem 1

x + -12.04819277 = 10.725598681 Simplifying x + -12.04819277 = 10.725598681 Reorder the terms: -12.04819277 + x = 10.725598681 Solving -12.04819277 + x = 10.725598681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.04819277' to each side of the equation. -12.04819277 + 12.04819277 + x = 10.725598681 + 12.04819277 Combine like terms: -12.04819277 + 12.04819277 = 0.00000000 0.00000000 + x = 10.725598681 + 12.04819277 x = 10.725598681 + 12.04819277 Combine like terms: 10.725598681 + 12.04819277 = 22.773791451 x = 22.773791451 Simplifying x = 22.773791451

Subproblem 2

x + -12.04819277 = -10.725598681 Simplifying x + -12.04819277 = -10.725598681 Reorder the terms: -12.04819277 + x = -10.725598681 Solving -12.04819277 + x = -10.725598681 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.04819277' to each side of the equation. -12.04819277 + 12.04819277 + x = -10.725598681 + 12.04819277 Combine like terms: -12.04819277 + 12.04819277 = 0.00000000 0.00000000 + x = -10.725598681 + 12.04819277 x = -10.725598681 + 12.04819277 Combine like terms: -10.725598681 + 12.04819277 = 1.322594089 x = 1.322594089 Simplifying x = 1.322594089

Solution

The solution to the problem is based on the solutions from the subproblems. x = {22.773791451, 1.322594089}

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