-7x^2+20x-5=0

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Solution for -7x^2+20x-5=0 equation:


Simplifying
-7x2 + 20x + -5 = 0

Reorder the terms:
-5 + 20x + -7x2 = 0

Solving
-5 + 20x + -7x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-7 the coefficient of the squared term: 

Divide each side by '-7'.
0.7142857143 + -2.857142857x + x2 = 0

Move the constant term to the right:

Add '-0.7142857143' to each side of the equation.
0.7142857143 + -2.857142857x + -0.7142857143 + x2 = 0 + -0.7142857143

Reorder the terms:
0.7142857143 + -0.7142857143 + -2.857142857x + x2 = 0 + -0.7142857143

Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000
0.0000000000 + -2.857142857x + x2 = 0 + -0.7142857143
-2.857142857x + x2 = 0 + -0.7142857143

Combine like terms: 0 + -0.7142857143 = -0.7142857143
-2.857142857x + x2 = -0.7142857143

The x term is -2.857142857x.  Take half its coefficient (-1.428571429).
Square it (2.040816328) and add it to both sides.

Add '2.040816328' to each side of the equation.
-2.857142857x + 2.040816328 + x2 = -0.7142857143 + 2.040816328

Reorder the terms:
2.040816328 + -2.857142857x + x2 = -0.7142857143 + 2.040816328

Combine like terms: -0.7142857143 + 2.040816328 = 1.3265306137
2.040816328 + -2.857142857x + x2 = 1.3265306137

Factor a perfect square on the left side:
(x + -1.428571429)(x + -1.428571429) = 1.3265306137

Calculate the square root of the right side: 1.151751108

Break this problem into two subproblems by setting 
(x + -1.428571429) equal to 1.151751108 and -1.151751108.

Subproblem 1

x + -1.428571429 = 1.151751108 Simplifying x + -1.428571429 = 1.151751108 Reorder the terms: -1.428571429 + x = 1.151751108 Solving -1.428571429 + x = 1.151751108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = 1.151751108 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = 1.151751108 + 1.428571429 x = 1.151751108 + 1.428571429 Combine like terms: 1.151751108 + 1.428571429 = 2.580322537 x = 2.580322537 Simplifying x = 2.580322537

Subproblem 2

x + -1.428571429 = -1.151751108 Simplifying x + -1.428571429 = -1.151751108 Reorder the terms: -1.428571429 + x = -1.151751108 Solving -1.428571429 + x = -1.151751108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.428571429' to each side of the equation. -1.428571429 + 1.428571429 + x = -1.151751108 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = -1.151751108 + 1.428571429 x = -1.151751108 + 1.428571429 Combine like terms: -1.151751108 + 1.428571429 = 0.276820321 x = 0.276820321 Simplifying x = 0.276820321

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.580322537, 0.276820321}

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