7x^2-34x+5=0

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Solution for 7x^2-34x+5=0 equation:


Simplifying
7x2 + -34x + 5 = 0

Reorder the terms:
5 + -34x + 7x2 = 0

Solving
5 + -34x + 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 + -4.857142857x + x2 = 0

Move the constant term to the right:

Add '-0.7142857143' to each side of the equation.
0.7142857143 + -4.857142857x + -0.7142857143 + x2 = 0 + -0.7142857143

Reorder the terms:
0.7142857143 + -0.7142857143 + -4.857142857x + x2 = 0 + -0.7142857143

Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000
0.0000000000 + -4.857142857x + x2 = 0 + -0.7142857143
-4.857142857x + x2 = 0 + -0.7142857143

Combine like terms: 0 + -0.7142857143 = -0.7142857143
-4.857142857x + x2 = -0.7142857143

The x term is -4.857142857x.  Take half its coefficient (-2.428571429).
Square it (5.897959186) and add it to both sides.

Add '5.897959186' to each side of the equation.
-4.857142857x + 5.897959186 + x2 = -0.7142857143 + 5.897959186

Reorder the terms:
5.897959186 + -4.857142857x + x2 = -0.7142857143 + 5.897959186

Combine like terms: -0.7142857143 + 5.897959186 = 5.1836734717
5.897959186 + -4.857142857x + x2 = 5.1836734717

Factor a perfect square on the left side:
(x + -2.428571429)(x + -2.428571429) = 5.1836734717

Calculate the square root of the right side: 2.276768208

Break this problem into two subproblems by setting 
(x + -2.428571429) equal to 2.276768208 and -2.276768208.

Subproblem 1

x + -2.428571429 = 2.276768208 Simplifying x + -2.428571429 = 2.276768208 Reorder the terms: -2.428571429 + x = 2.276768208 Solving -2.428571429 + x = 2.276768208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.428571429' to each side of the equation. -2.428571429 + 2.428571429 + x = 2.276768208 + 2.428571429 Combine like terms: -2.428571429 + 2.428571429 = 0.000000000 0.000000000 + x = 2.276768208 + 2.428571429 x = 2.276768208 + 2.428571429 Combine like terms: 2.276768208 + 2.428571429 = 4.705339637 x = 4.705339637 Simplifying x = 4.705339637

Subproblem 2

x + -2.428571429 = -2.276768208 Simplifying x + -2.428571429 = -2.276768208 Reorder the terms: -2.428571429 + x = -2.276768208 Solving -2.428571429 + x = -2.276768208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.428571429' to each side of the equation. -2.428571429 + 2.428571429 + x = -2.276768208 + 2.428571429 Combine like terms: -2.428571429 + 2.428571429 = 0.000000000 0.000000000 + x = -2.276768208 + 2.428571429 x = -2.276768208 + 2.428571429 Combine like terms: -2.276768208 + 2.428571429 = 0.151803221 x = 0.151803221 Simplifying x = 0.151803221

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.705339637, 0.151803221}

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