7x^2-x-.5=0

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


Simplifying
7x2 + -1x + -0.5 = 0

Reorder the terms:
-0.5 + -1x + 7x2 = 0

Solving
-0.5 + -1x + 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'.
-0.07142857143 + -0.1428571429x + x2 = 0

Move the constant term to the right:

Add '0.07142857143' to each side of the equation.
-0.07142857143 + -0.1428571429x + 0.07142857143 + x2 = 0 + 0.07142857143

Reorder the terms:
-0.07142857143 + 0.07142857143 + -0.1428571429x + x2 = 0 + 0.07142857143

Combine like terms: -0.07142857143 + 0.07142857143 = 0.00000000000
0.00000000000 + -0.1428571429x + x2 = 0 + 0.07142857143
-0.1428571429x + x2 = 0 + 0.07142857143

Combine like terms: 0 + 0.07142857143 = 0.07142857143
-0.1428571429x + x2 = 0.07142857143

The x term is -0.1428571429x.  Take half its coefficient (-0.07142857145).
Square it (0.005102040819) and add it to both sides.

Add '0.005102040819' to each side of the equation.
-0.1428571429x + 0.005102040819 + x2 = 0.07142857143 + 0.005102040819

Reorder the terms:
0.005102040819 + -0.1428571429x + x2 = 0.07142857143 + 0.005102040819

Combine like terms: 0.07142857143 + 0.005102040819 = 0.076530612249
0.005102040819 + -0.1428571429x + x2 = 0.076530612249

Factor a perfect square on the left side:
(x + -0.07142857145)(x + -0.07142857145) = 0.076530612249

Calculate the square root of the right side: 0.276641668

Break this problem into two subproblems by setting 
(x + -0.07142857145) equal to 0.276641668 and -0.276641668.

Subproblem 1

x + -0.07142857145 = 0.276641668 Simplifying x + -0.07142857145 = 0.276641668 Reorder the terms: -0.07142857145 + x = 0.276641668 Solving -0.07142857145 + x = 0.276641668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = 0.276641668 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = 0.276641668 + 0.07142857145 x = 0.276641668 + 0.07142857145 Combine like terms: 0.276641668 + 0.07142857145 = 0.34807023945 x = 0.34807023945 Simplifying x = 0.34807023945

Subproblem 2

x + -0.07142857145 = -0.276641668 Simplifying x + -0.07142857145 = -0.276641668 Reorder the terms: -0.07142857145 + x = -0.276641668 Solving -0.07142857145 + x = -0.276641668 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = -0.276641668 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = -0.276641668 + 0.07142857145 x = -0.276641668 + 0.07142857145 Combine like terms: -0.276641668 + 0.07142857145 = -0.20521309655 x = -0.20521309655 Simplifying x = -0.20521309655

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.34807023945, -0.20521309655}

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