7x^2-x-0.7=0

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Solution for 7x^2-x-0.7=0 equation:


Simplifying
7x2 + -1x + -0.7 = 0

Reorder the terms:
-0.7 + -1x + 7x2 = 0

Solving
-0.7 + -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'.
-0.1 + -0.1428571429x + x2 = 0

Move the constant term to the right:

Add '0.1' to each side of the equation.
-0.1 + -0.1428571429x + 0.1 + x2 = 0 + 0.1

Reorder the terms:
-0.1 + 0.1 + -0.1428571429x + x2 = 0 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + -0.1428571429x + x2 = 0 + 0.1
-0.1428571429x + x2 = 0 + 0.1

Combine like terms: 0 + 0.1 = 0.1
-0.1428571429x + x2 = 0.1

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 = 0.1 + 0.005102040819

Reorder the terms:
0.005102040819 + -0.1428571429x + x2 = 0.1 + 0.005102040819

Combine like terms: 0.1 + 0.005102040819 = 0.105102040819
0.005102040819 + -0.1428571429x + x2 = 0.105102040819

Factor a perfect square on the left side:
(x + -0.07142857145)(x + -0.07142857145) = 0.105102040819

Calculate the square root of the right side: 0.324194449

Break this problem into two subproblems by setting 
(x + -0.07142857145) equal to 0.324194449 and -0.324194449.

Subproblem 1

x + -0.07142857145 = 0.324194449 Simplifying x + -0.07142857145 = 0.324194449 Reorder the terms: -0.07142857145 + x = 0.324194449 Solving -0.07142857145 + x = 0.324194449 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 = 0.324194449 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = 0.324194449 + 0.07142857145 x = 0.324194449 + 0.07142857145 Combine like terms: 0.324194449 + 0.07142857145 = 0.39562302045 x = 0.39562302045 Simplifying x = 0.39562302045

Subproblem 2

x + -0.07142857145 = -0.324194449 Simplifying x + -0.07142857145 = -0.324194449 Reorder the terms: -0.07142857145 + x = -0.324194449 Solving -0.07142857145 + x = -0.324194449 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 = -0.324194449 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = -0.324194449 + 0.07142857145 x = -0.324194449 + 0.07142857145 Combine like terms: -0.324194449 + 0.07142857145 = -0.25276587755 x = -0.25276587755 Simplifying x = -0.25276587755

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.39562302045, -0.25276587755}

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