3x^2+7x+7x+17=59

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Solution for 3x^2+7x+7x+17=59 equation:


Simplifying
3x2 + 7x + 7x + 17 = 59

Reorder the terms:
17 + 7x + 7x + 3x2 = 59

Combine like terms: 7x + 7x = 14x
17 + 14x + 3x2 = 59

Solving
17 + 14x + 3x2 = 59

Solving for variable 'x'.

Reorder the terms:
17 + -59 + 14x + 3x2 = 59 + -59

Combine like terms: 17 + -59 = -42
-42 + 14x + 3x2 = 59 + -59

Combine like terms: 59 + -59 = 0
-42 + 14x + 3x2 = 0

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

Divide each side by '3'.
-14 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 4.666666667x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + 4.666666667x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 4.666666667x + x2 = 0 + 14
4.666666667x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
4.666666667x + x2 = 14

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 = 14 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = 14 + 5.444444448

Combine like terms: 14 + 5.444444448 = 19.444444448
5.444444448 + 4.666666667x + x2 = 19.444444448

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 19.444444448

Calculate the square root of the right side: 4.409585519

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 4.409585519 and -4.409585519.

Subproblem 1

x + 2.333333334 = 4.409585519 Simplifying x + 2.333333334 = 4.409585519 Reorder the terms: 2.333333334 + x = 4.409585519 Solving 2.333333334 + x = 4.409585519 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 = 4.409585519 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = 4.409585519 + -2.333333334 x = 4.409585519 + -2.333333334 Combine like terms: 4.409585519 + -2.333333334 = 2.076252185 x = 2.076252185 Simplifying x = 2.076252185

Subproblem 2

x + 2.333333334 = -4.409585519 Simplifying x + 2.333333334 = -4.409585519 Reorder the terms: 2.333333334 + x = -4.409585519 Solving 2.333333334 + x = -4.409585519 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 = -4.409585519 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = -4.409585519 + -2.333333334 x = -4.409585519 + -2.333333334 Combine like terms: -4.409585519 + -2.333333334 = -6.742918853 x = -6.742918853 Simplifying x = -6.742918853

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.076252185, -6.742918853}

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