14x^2+2x-21=0

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Solution for 14x^2+2x-21=0 equation:


Simplifying
14x2 + 2x + -21 = 0

Reorder the terms:
-21 + 2x + 14x2 = 0

Solving
-21 + 2x + 14x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
14 the coefficient of the squared term: 

Divide each side by '14'.
-1.5 + 0.1428571429x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 0.1428571429x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 0.1428571429x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 0.1428571429x + x2 = 0 + 1.5
0.1428571429x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
0.1428571429x + x2 = 1.5

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 = 1.5 + 0.005102040819

Reorder the terms:
0.005102040819 + 0.1428571429x + x2 = 1.5 + 0.005102040819

Combine like terms: 1.5 + 0.005102040819 = 1.505102040819
0.005102040819 + 0.1428571429x + x2 = 1.505102040819

Factor a perfect square on the left side:
(x + 0.07142857145)(x + 0.07142857145) = 1.505102040819

Calculate the square root of the right side: 1.226826003

Break this problem into two subproblems by setting 
(x + 0.07142857145) equal to 1.226826003 and -1.226826003.

Subproblem 1

x + 0.07142857145 = 1.226826003 Simplifying x + 0.07142857145 = 1.226826003 Reorder the terms: 0.07142857145 + x = 1.226826003 Solving 0.07142857145 + x = 1.226826003 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 = 1.226826003 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + x = 1.226826003 + -0.07142857145 x = 1.226826003 + -0.07142857145 Combine like terms: 1.226826003 + -0.07142857145 = 1.15539743155 x = 1.15539743155 Simplifying x = 1.15539743155

Subproblem 2

x + 0.07142857145 = -1.226826003 Simplifying x + 0.07142857145 = -1.226826003 Reorder the terms: 0.07142857145 + x = -1.226826003 Solving 0.07142857145 + x = -1.226826003 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 = -1.226826003 + -0.07142857145 Combine like terms: 0.07142857145 + -0.07142857145 = 0.00000000000 0.00000000000 + x = -1.226826003 + -0.07142857145 x = -1.226826003 + -0.07142857145 Combine like terms: -1.226826003 + -0.07142857145 = -1.29825457445 x = -1.29825457445 Simplifying x = -1.29825457445

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.15539743155, -1.29825457445}

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