-3x^2+14x+49=42

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Solution for -3x^2+14x+49=42 equation: 


Simplifying
-3x2 + 14x + 49 = 42

Reorder the terms:
49 + 14x + -3x2 = 42

Solving
49 + 14x + -3x2 = 42

Solving for variable 'x'.

Reorder the terms:
49 + -42 + 14x + -3x2 = 42 + -42

Combine like terms: 49 + -42 = 7
7 + 14x + -3x2 = 42 + -42

Combine like terms: 42 + -42 = 0
7 + 14x + -3x2 = 0

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

Divide each side by '-3'.
-2.333333333 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + -4.666666667x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + -4.666666667x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + -4.666666667x + x2 = 0 + 2.333333333
-4.666666667x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
-4.666666667x + x2 = 2.333333333

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 = 2.333333333 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = 2.333333333 + 5.444444448

Combine like terms: 2.333333333 + 5.444444448 = 7.777777781
5.444444448 + -4.666666667x + x2 = 7.777777781

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = 7.777777781

Calculate the square root of the right side: 2.788866756

Break this problem into two subproblems by setting 
(x + -2.333333334) equal to 2.788866756 and -2.788866756.


Subproblem 1
x + -2.333333334 = 2.788866756

Simplifying
x + -2.333333334 = 2.788866756

Reorder the terms:
-2.333333334 + x = 2.788866756

Solving
-2.333333334 + x = 2.788866756

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 = 2.788866756 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = 2.788866756 + 2.333333334
x = 2.788866756 + 2.333333334

Combine like terms: 2.788866756 + 2.333333334 = 5.12220009
x = 5.12220009

Simplifying
x = 5.12220009


Subproblem 2
x + -2.333333334 = -2.788866756

Simplifying
x + -2.333333334 = -2.788866756

Reorder the terms:
-2.333333334 + x = -2.788866756

Solving
-2.333333334 + x = -2.788866756

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 = -2.788866756 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = -2.788866756 + 2.333333334
x = -2.788866756 + 2.333333334

Combine like terms: -2.788866756 + 2.333333334 = -0.455533422
x = -0.455533422

Simplifying
x = -0.455533422


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.12220009, -0.455533422}

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