7x^2-62x+9=0

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Solution for 7x^2-62x+9=0 equation: 


Simplifying
7x2 + -62x + 9 = 0

Reorder the terms:
9 + -62x + 7x2 = 0

Solving
9 + -62x + 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 + -8.857142857x + x2 = 0

Move the constant term to the right:

Add '-1.285714286' to each side of the equation.
1.285714286 + -8.857142857x + -1.285714286 + x2 = 0 + -1.285714286

Reorder the terms:
1.285714286 + -1.285714286 + -8.857142857x + x2 = 0 + -1.285714286

Combine like terms: 1.285714286 + -1.285714286 = 0.000000000
0.000000000 + -8.857142857x + x2 = 0 + -1.285714286
-8.857142857x + x2 = 0 + -1.285714286

Combine like terms: 0 + -1.285714286 = -1.285714286
-8.857142857x + x2 = -1.285714286

The x term is -8.857142857x.  Take half its coefficient (-4.428571429).
Square it (19.61224490) and add it to both sides.

Add '19.61224490' to each side of the equation.
-8.857142857x + 19.61224490 + x2 = -1.285714286 + 19.61224490

Reorder the terms:
19.61224490 + -8.857142857x + x2 = -1.285714286 + 19.61224490

Combine like terms: -1.285714286 + 19.61224490 = 18.326530614
19.61224490 + -8.857142857x + x2 = 18.326530614

Factor a perfect square on the left side:
(x + -4.428571429)(x + -4.428571429) = 18.326530614

Calculate the square root of the right side: 4.280949733

Break this problem into two subproblems by setting 
(x + -4.428571429) equal to 4.280949733 and -4.280949733.


Subproblem 1
x + -4.428571429 = 4.280949733

Simplifying
x + -4.428571429 = 4.280949733

Reorder the terms:
-4.428571429 + x = 4.280949733

Solving
-4.428571429 + x = 4.280949733

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4.428571429' to each side of the equation.
-4.428571429 + 4.428571429 + x = 4.280949733 + 4.428571429

Combine like terms: -4.428571429 + 4.428571429 = 0.000000000
0.000000000 + x = 4.280949733 + 4.428571429
x = 4.280949733 + 4.428571429

Combine like terms: 4.280949733 + 4.428571429 = 8.709521162
x = 8.709521162

Simplifying
x = 8.709521162


Subproblem 2
x + -4.428571429 = -4.280949733

Simplifying
x + -4.428571429 = -4.280949733

Reorder the terms:
-4.428571429 + x = -4.280949733

Solving
-4.428571429 + x = -4.280949733

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4.428571429' to each side of the equation.
-4.428571429 + 4.428571429 + x = -4.280949733 + 4.428571429

Combine like terms: -4.428571429 + 4.428571429 = 0.000000000
0.000000000 + x = -4.280949733 + 4.428571429
x = -4.280949733 + 4.428571429

Combine like terms: -4.280949733 + 4.428571429 = 0.147621696
x = 0.147621696

Simplifying
x = 0.147621696


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.709521162, 0.147621696}

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