7x^2-20x+9=0

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Solution for 7x^2-20x+9=0 equation:


Simplifying
7x2 + -20x + 9 = 0

Reorder the terms:
9 + -20x + 7x2 = 0

Solving
9 + -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'.
1.285714286 + -2.857142857x + x2 = 0

Move the constant term to the right:

Add '-1.285714286' to each side of the equation.
1.285714286 + -2.857142857x + -1.285714286 + x2 = 0 + -1.285714286

Reorder the terms:
1.285714286 + -1.285714286 + -2.857142857x + x2 = 0 + -1.285714286

Combine like terms: 1.285714286 + -1.285714286 = 0.000000000
0.000000000 + -2.857142857x + x2 = 0 + -1.285714286
-2.857142857x + x2 = 0 + -1.285714286

Combine like terms: 0 + -1.285714286 = -1.285714286
-2.857142857x + x2 = -1.285714286

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 = -1.285714286 + 2.040816328

Reorder the terms:
2.040816328 + -2.857142857x + x2 = -1.285714286 + 2.040816328

Combine like terms: -1.285714286 + 2.040816328 = 0.755102042
2.040816328 + -2.857142857x + x2 = 0.755102042

Factor a perfect square on the left side:
(x + -1.428571429)(x + -1.428571429) = 0.755102042

Calculate the square root of the right side: 0.868966076

Break this problem into two subproblems by setting 
(x + -1.428571429) equal to 0.868966076 and -0.868966076.

Subproblem 1

x + -1.428571429 = 0.868966076 Simplifying x + -1.428571429 = 0.868966076 Reorder the terms: -1.428571429 + x = 0.868966076 Solving -1.428571429 + x = 0.868966076 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 = 0.868966076 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = 0.868966076 + 1.428571429 x = 0.868966076 + 1.428571429 Combine like terms: 0.868966076 + 1.428571429 = 2.297537505 x = 2.297537505 Simplifying x = 2.297537505

Subproblem 2

x + -1.428571429 = -0.868966076 Simplifying x + -1.428571429 = -0.868966076 Reorder the terms: -1.428571429 + x = -0.868966076 Solving -1.428571429 + x = -0.868966076 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 = -0.868966076 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + x = -0.868966076 + 1.428571429 x = -0.868966076 + 1.428571429 Combine like terms: -0.868966076 + 1.428571429 = 0.559605353 x = 0.559605353 Simplifying x = 0.559605353

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.297537505, 0.559605353}

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