9x^2-8x-14=0

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Solution for 9x^2-8x-14=0 equation:


Simplifying
9x2 + -8x + -14 = 0

Reorder the terms:
-14 + -8x + 9x2 = 0

Solving
-14 + -8x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-1.555555556 + -0.8888888889x + x2 = 0

Move the constant term to the right:

Add '1.555555556' to each side of the equation.
-1.555555556 + -0.8888888889x + 1.555555556 + x2 = 0 + 1.555555556

Reorder the terms:
-1.555555556 + 1.555555556 + -0.8888888889x + x2 = 0 + 1.555555556

Combine like terms: -1.555555556 + 1.555555556 = 0.000000000
0.000000000 + -0.8888888889x + x2 = 0 + 1.555555556
-0.8888888889x + x2 = 0 + 1.555555556

Combine like terms: 0 + 1.555555556 = 1.555555556
-0.8888888889x + x2 = 1.555555556

The x term is -0.8888888889x.  Take half its coefficient (-0.4444444445).
Square it (0.1975308642) and add it to both sides.

Add '0.1975308642' to each side of the equation.
-0.8888888889x + 0.1975308642 + x2 = 1.555555556 + 0.1975308642

Reorder the terms:
0.1975308642 + -0.8888888889x + x2 = 1.555555556 + 0.1975308642

Combine like terms: 1.555555556 + 0.1975308642 = 1.7530864202
0.1975308642 + -0.8888888889x + x2 = 1.7530864202

Factor a perfect square on the left side:
(x + -0.4444444445)(x + -0.4444444445) = 1.7530864202

Calculate the square root of the right side: 1.324041699

Break this problem into two subproblems by setting 
(x + -0.4444444445) equal to 1.324041699 and -1.324041699.

Subproblem 1

x + -0.4444444445 = 1.324041699 Simplifying x + -0.4444444445 = 1.324041699 Reorder the terms: -0.4444444445 + x = 1.324041699 Solving -0.4444444445 + x = 1.324041699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + x = 1.324041699 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = 1.324041699 + 0.4444444445 x = 1.324041699 + 0.4444444445 Combine like terms: 1.324041699 + 0.4444444445 = 1.7684861435 x = 1.7684861435 Simplifying x = 1.7684861435

Subproblem 2

x + -0.4444444445 = -1.324041699 Simplifying x + -0.4444444445 = -1.324041699 Reorder the terms: -0.4444444445 + x = -1.324041699 Solving -0.4444444445 + x = -1.324041699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + x = -1.324041699 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = -1.324041699 + 0.4444444445 x = -1.324041699 + 0.4444444445 Combine like terms: -1.324041699 + 0.4444444445 = -0.8795972545 x = -0.8795972545 Simplifying x = -0.8795972545

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.7684861435, -0.8795972545}

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