-3x^2+14x+34=-16

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Solution for -3x^2+14x+34=-16 equation: 


Simplifying
-3x2 + 14x + 34 = -16

Reorder the terms:
34 + 14x + -3x2 = -16

Solving
34 + 14x + -3x2 = -16

Solving for variable 'x'.

Reorder the terms:
34 + 16 + 14x + -3x2 = -16 + 16

Combine like terms: 34 + 16 = 50
50 + 14x + -3x2 = -16 + 16

Combine like terms: -16 + 16 = 0
50 + 14x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-16.66666667 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '16.66666667' to each side of the equation.
-16.66666667 + -4.666666667x + 16.66666667 + x2 = 0 + 16.66666667

Reorder the terms:
-16.66666667 + 16.66666667 + -4.666666667x + x2 = 0 + 16.66666667

Combine like terms: -16.66666667 + 16.66666667 = 0.00000000
0.00000000 + -4.666666667x + x2 = 0 + 16.66666667
-4.666666667x + x2 = 0 + 16.66666667

Combine like terms: 0 + 16.66666667 = 16.66666667
-4.666666667x + x2 = 16.66666667

The x term is -4.666666667x.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667x + 5.444444448 + x2 = 16.66666667 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = 16.66666667 + 5.444444448

Combine like terms: 16.66666667 + 5.444444448 = 22.111111118
5.444444448 + -4.666666667x + x2 = 22.111111118

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = 22.111111118

Calculate the square root of the right side: 4.702245327

Break this problem into two subproblems by setting 
(x + -2.333333334) equal to 4.702245327 and -4.702245327.


Subproblem 1
x + -2.333333334 = 4.702245327

Simplifying
x + -2.333333334 = 4.702245327

Reorder the terms:
-2.333333334 + x = 4.702245327

Solving
-2.333333334 + x = 4.702245327

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = 4.702245327 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = 4.702245327 + 2.333333334
x = 4.702245327 + 2.333333334

Combine like terms: 4.702245327 + 2.333333334 = 7.035578661
x = 7.035578661

Simplifying
x = 7.035578661


Subproblem 2
x + -2.333333334 = -4.702245327

Simplifying
x + -2.333333334 = -4.702245327

Reorder the terms:
-2.333333334 + x = -4.702245327

Solving
-2.333333334 + x = -4.702245327

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = -4.702245327 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = -4.702245327 + 2.333333334
x = -4.702245327 + 2.333333334

Combine like terms: -4.702245327 + 2.333333334 = -2.368911993
x = -2.368911993

Simplifying
x = -2.368911993


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.035578661, -2.368911993}

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