7x^2-23x+10=0

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Solution for 7x^2-23x+10=0 equation:


Simplifying
7x2 + -23x + 10 = 0

Reorder the terms:
10 + -23x + 7x2 = 0

Solving
10 + -23x + 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'.
1.428571429 + -3.285714286x + x2 = 0

Move the constant term to the right:

Add '-1.428571429' to each side of the equation.
1.428571429 + -3.285714286x + -1.428571429 + x2 = 0 + -1.428571429

Reorder the terms:
1.428571429 + -1.428571429 + -3.285714286x + x2 = 0 + -1.428571429

Combine like terms: 1.428571429 + -1.428571429 = 0.000000000
0.000000000 + -3.285714286x + x2 = 0 + -1.428571429
-3.285714286x + x2 = 0 + -1.428571429

Combine like terms: 0 + -1.428571429 = -1.428571429
-3.285714286x + x2 = -1.428571429

The x term is -3.285714286x.  Take half its coefficient (-1.642857143).
Square it (2.698979592) and add it to both sides.

Add '2.698979592' to each side of the equation.
-3.285714286x + 2.698979592 + x2 = -1.428571429 + 2.698979592

Reorder the terms:
2.698979592 + -3.285714286x + x2 = -1.428571429 + 2.698979592

Combine like terms: -1.428571429 + 2.698979592 = 1.270408163
2.698979592 + -3.285714286x + x2 = 1.270408163

Factor a perfect square on the left side:
(x + -1.642857143)(x + -1.642857143) = 1.270408163

Calculate the square root of the right side: 1.127123845

Break this problem into two subproblems by setting 
(x + -1.642857143) equal to 1.127123845 and -1.127123845.

Subproblem 1

x + -1.642857143 = 1.127123845 Simplifying x + -1.642857143 = 1.127123845 Reorder the terms: -1.642857143 + x = 1.127123845 Solving -1.642857143 + x = 1.127123845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.642857143' to each side of the equation. -1.642857143 + 1.642857143 + x = 1.127123845 + 1.642857143 Combine like terms: -1.642857143 + 1.642857143 = 0.000000000 0.000000000 + x = 1.127123845 + 1.642857143 x = 1.127123845 + 1.642857143 Combine like terms: 1.127123845 + 1.642857143 = 2.769980988 x = 2.769980988 Simplifying x = 2.769980988

Subproblem 2

x + -1.642857143 = -1.127123845 Simplifying x + -1.642857143 = -1.127123845 Reorder the terms: -1.642857143 + x = -1.127123845 Solving -1.642857143 + x = -1.127123845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.642857143' to each side of the equation. -1.642857143 + 1.642857143 + x = -1.127123845 + 1.642857143 Combine like terms: -1.642857143 + 1.642857143 = 0.000000000 0.000000000 + x = -1.127123845 + 1.642857143 x = -1.127123845 + 1.642857143 Combine like terms: -1.127123845 + 1.642857143 = 0.515733298 x = 0.515733298 Simplifying x = 0.515733298

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.769980988, 0.515733298}

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