(14x^2-22)-(14x+5)=

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Solution for (14x^2-22)-(14x+5)= equation:


Simplifying
(14x2 + -22) + -1(14x + 5) = 0

Reorder the terms:
(-22 + 14x2) + -1(14x + 5) = 0

Remove parenthesis around (-22 + 14x2)
-22 + 14x2 + -1(14x + 5) = 0

Reorder the terms:
-22 + 14x2 + -1(5 + 14x) = 0
-22 + 14x2 + (5 * -1 + 14x * -1) = 0
-22 + 14x2 + (-5 + -14x) = 0

Reorder the terms:
-22 + -5 + -14x + 14x2 = 0

Combine like terms: -22 + -5 = -27
-27 + -14x + 14x2 = 0

Solving
-27 + -14x + 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'.
-1.928571429 + -1x + x2 = 0

Move the constant term to the right:

Add '1.928571429' to each side of the equation.
-1.928571429 + -1x + 1.928571429 + x2 = 0 + 1.928571429

Reorder the terms:
-1.928571429 + 1.928571429 + -1x + x2 = 0 + 1.928571429

Combine like terms: -1.928571429 + 1.928571429 = 0.000000000
0.000000000 + -1x + x2 = 0 + 1.928571429
-1x + x2 = 0 + 1.928571429

Combine like terms: 0 + 1.928571429 = 1.928571429
-1x + x2 = 1.928571429

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 1.928571429 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 1.928571429 + 0.25

Combine like terms: 1.928571429 + 0.25 = 2.178571429
0.25 + -1x + x2 = 2.178571429

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 2.178571429

Calculate the square root of the right side: 1.475998452

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.475998452 and -1.475998452.

Subproblem 1

x + -0.5 = 1.475998452 Simplifying x + -0.5 = 1.475998452 Reorder the terms: -0.5 + x = 1.475998452 Solving -0.5 + x = 1.475998452 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.475998452 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.475998452 + 0.5 x = 1.475998452 + 0.5 Combine like terms: 1.475998452 + 0.5 = 1.975998452 x = 1.975998452 Simplifying x = 1.975998452

Subproblem 2

x + -0.5 = -1.475998452 Simplifying x + -0.5 = -1.475998452 Reorder the terms: -0.5 + x = -1.475998452 Solving -0.5 + x = -1.475998452 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.475998452 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.475998452 + 0.5 x = -1.475998452 + 0.5 Combine like terms: -1.475998452 + 0.5 = -0.975998452 x = -0.975998452 Simplifying x = -0.975998452

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.975998452, -0.975998452}

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