0=0.0652x^2-1.724x+5.1602

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Solution for 0=0.0652x^2-1.724x+5.1602 equation:


Simplifying
0 = 0.0652x2 + -1.724x + 5.1602

Reorder the terms:
0 = 5.1602 + -1.724x + 0.0652x2

Solving
0 = 5.1602 + -1.724x + 0.0652x2

Solving for variable 'x'.

Combine like terms: 0 + -5.1602 = -5.1602
-5.1602 + 1.724x + -0.0652x2 = 5.1602 + -1.724x + 0.0652x2 + -5.1602 + 1.724x + -0.0652x2

Reorder the terms:
-5.1602 + 1.724x + -0.0652x2 = 5.1602 + -5.1602 + -1.724x + 1.724x + 0.0652x2 + -0.0652x2

Combine like terms: 5.1602 + -5.1602 = 0.0000
-5.1602 + 1.724x + -0.0652x2 = 0.0000 + -1.724x + 1.724x + 0.0652x2 + -0.0652x2
-5.1602 + 1.724x + -0.0652x2 = -1.724x + 1.724x + 0.0652x2 + -0.0652x2

Combine like terms: -1.724x + 1.724x = 0.000
-5.1602 + 1.724x + -0.0652x2 = 0.000 + 0.0652x2 + -0.0652x2
-5.1602 + 1.724x + -0.0652x2 = 0.0652x2 + -0.0652x2

Combine like terms: 0.0652x2 + -0.0652x2 = 0.0000
-5.1602 + 1.724x + -0.0652x2 = 0.0000

Begin completing the square.  Divide all terms by
-0.0652 the coefficient of the squared term: 

Divide each side by '-0.0652'.
79.14417178 + -26.44171779x + x2 = 0

Move the constant term to the right:

Add '-79.14417178' to each side of the equation.
79.14417178 + -26.44171779x + -79.14417178 + x2 = 0 + -79.14417178

Reorder the terms:
79.14417178 + -79.14417178 + -26.44171779x + x2 = 0 + -79.14417178

Combine like terms: 79.14417178 + -79.14417178 = 0.00000000
0.00000000 + -26.44171779x + x2 = 0 + -79.14417178
-26.44171779x + x2 = 0 + -79.14417178

Combine like terms: 0 + -79.14417178 = -79.14417178
-26.44171779x + x2 = -79.14417178

The x term is -26.44171779x.  Take half its coefficient (-13.2208589).
Square it (174.7911101) and add it to both sides.

Add '174.7911101' to each side of the equation.
-26.44171779x + 174.7911101 + x2 = -79.14417178 + 174.7911101

Reorder the terms:
174.7911101 + -26.44171779x + x2 = -79.14417178 + 174.7911101

Combine like terms: -79.14417178 + 174.7911101 = 95.64693832
174.7911101 + -26.44171779x + x2 = 95.64693832

Factor a perfect square on the left side:
(x + -13.2208589)(x + -13.2208589) = 95.64693832

Calculate the square root of the right side: 9.779925272

Break this problem into two subproblems by setting 
(x + -13.2208589) equal to 9.779925272 and -9.779925272.

Subproblem 1

x + -13.2208589 = 9.779925272 Simplifying x + -13.2208589 = 9.779925272 Reorder the terms: -13.2208589 + x = 9.779925272 Solving -13.2208589 + x = 9.779925272 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.2208589' to each side of the equation. -13.2208589 + 13.2208589 + x = 9.779925272 + 13.2208589 Combine like terms: -13.2208589 + 13.2208589 = 0.0000000 0.0000000 + x = 9.779925272 + 13.2208589 x = 9.779925272 + 13.2208589 Combine like terms: 9.779925272 + 13.2208589 = 23.000784172 x = 23.000784172 Simplifying x = 23.000784172

Subproblem 2

x + -13.2208589 = -9.779925272 Simplifying x + -13.2208589 = -9.779925272 Reorder the terms: -13.2208589 + x = -9.779925272 Solving -13.2208589 + x = -9.779925272 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13.2208589' to each side of the equation. -13.2208589 + 13.2208589 + x = -9.779925272 + 13.2208589 Combine like terms: -13.2208589 + 13.2208589 = 0.0000000 0.0000000 + x = -9.779925272 + 13.2208589 x = -9.779925272 + 13.2208589 Combine like terms: -9.779925272 + 13.2208589 = 3.440933628 x = 3.440933628 Simplifying x = 3.440933628

Solution

The solution to the problem is based on the solutions from the subproblems. x = {23.000784172, 3.440933628}

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