65=0.04x^2-3x+104

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Solution for 65=0.04x^2-3x+104 equation:


Simplifying
65 = 0.04x2 + -3x + 104

Reorder the terms:
65 = 104 + -3x + 0.04x2

Solving
65 = 104 + -3x + 0.04x2

Solving for variable 'x'.

Combine like terms: 65 + -104 = -39
-39 + 3x + -0.04x2 = 104 + -3x + 0.04x2 + -104 + 3x + -0.04x2

Reorder the terms:
-39 + 3x + -0.04x2 = 104 + -104 + -3x + 3x + 0.04x2 + -0.04x2

Combine like terms: 104 + -104 = 0
-39 + 3x + -0.04x2 = 0 + -3x + 3x + 0.04x2 + -0.04x2
-39 + 3x + -0.04x2 = -3x + 3x + 0.04x2 + -0.04x2

Combine like terms: -3x + 3x = 0
-39 + 3x + -0.04x2 = 0 + 0.04x2 + -0.04x2
-39 + 3x + -0.04x2 = 0.04x2 + -0.04x2

Combine like terms: 0.04x2 + -0.04x2 = 0.00
-39 + 3x + -0.04x2 = 0.00

Begin completing the square.  Divide all terms by
-0.04 the coefficient of the squared term: 

Divide each side by '-0.04'.
975 + -75x + x2 = 0

Move the constant term to the right:

Add '-975' to each side of the equation.
975 + -75x + -975 + x2 = 0 + -975

Reorder the terms:
975 + -975 + -75x + x2 = 0 + -975

Combine like terms: 975 + -975 = 0
0 + -75x + x2 = 0 + -975
-75x + x2 = 0 + -975

Combine like terms: 0 + -975 = -975
-75x + x2 = -975

The x term is -75x.  Take half its coefficient (-37.5).
Square it (1406.25) and add it to both sides.

Add '1406.25' to each side of the equation.
-75x + 1406.25 + x2 = -975 + 1406.25

Reorder the terms:
1406.25 + -75x + x2 = -975 + 1406.25

Combine like terms: -975 + 1406.25 = 431.25
1406.25 + -75x + x2 = 431.25

Factor a perfect square on the left side:
(x + -37.5)(x + -37.5) = 431.25

Calculate the square root of the right side: 20.766559657

Break this problem into two subproblems by setting 
(x + -37.5) equal to 20.766559657 and -20.766559657.

Subproblem 1

x + -37.5 = 20.766559657 Simplifying x + -37.5 = 20.766559657 Reorder the terms: -37.5 + x = 20.766559657 Solving -37.5 + x = 20.766559657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '37.5' to each side of the equation. -37.5 + 37.5 + x = 20.766559657 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + x = 20.766559657 + 37.5 x = 20.766559657 + 37.5 Combine like terms: 20.766559657 + 37.5 = 58.266559657 x = 58.266559657 Simplifying x = 58.266559657

Subproblem 2

x + -37.5 = -20.766559657 Simplifying x + -37.5 = -20.766559657 Reorder the terms: -37.5 + x = -20.766559657 Solving -37.5 + x = -20.766559657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '37.5' to each side of the equation. -37.5 + 37.5 + x = -20.766559657 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + x = -20.766559657 + 37.5 x = -20.766559657 + 37.5 Combine like terms: -20.766559657 + 37.5 = 16.733440343 x = 16.733440343 Simplifying x = 16.733440343

Solution

The solution to the problem is based on the solutions from the subproblems. x = {58.266559657, 16.733440343}

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