9x^2+42x+16=0

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Solution for 9x^2+42x+16=0 equation:


Simplifying
9x2 + 42x + 16 = 0

Reorder the terms:
16 + 42x + 9x2 = 0

Solving
16 + 42x + 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'.
1.777777778 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '-1.777777778' to each side of the equation.
1.777777778 + 4.666666667x + -1.777777778 + x2 = 0 + -1.777777778

Reorder the terms:
1.777777778 + -1.777777778 + 4.666666667x + x2 = 0 + -1.777777778

Combine like terms: 1.777777778 + -1.777777778 = 0.000000000
0.000000000 + 4.666666667x + x2 = 0 + -1.777777778
4.666666667x + x2 = 0 + -1.777777778

Combine like terms: 0 + -1.777777778 = -1.777777778
4.666666667x + x2 = -1.777777778

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 = -1.777777778 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = -1.777777778 + 5.444444448

Combine like terms: -1.777777778 + 5.444444448 = 3.66666667
5.444444448 + 4.666666667x + x2 = 3.66666667

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 3.66666667

Calculate the square root of the right side: 1.914854216

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 1.914854216 and -1.914854216.

Subproblem 1

x + 2.333333334 = 1.914854216 Simplifying x + 2.333333334 = 1.914854216 Reorder the terms: 2.333333334 + x = 1.914854216 Solving 2.333333334 + x = 1.914854216 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 = 1.914854216 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = 1.914854216 + -2.333333334 x = 1.914854216 + -2.333333334 Combine like terms: 1.914854216 + -2.333333334 = -0.418479118 x = -0.418479118 Simplifying x = -0.418479118

Subproblem 2

x + 2.333333334 = -1.914854216 Simplifying x + 2.333333334 = -1.914854216 Reorder the terms: 2.333333334 + x = -1.914854216 Solving 2.333333334 + x = -1.914854216 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 = -1.914854216 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = -1.914854216 + -2.333333334 x = -1.914854216 + -2.333333334 Combine like terms: -1.914854216 + -2.333333334 = -4.24818755 x = -4.24818755 Simplifying x = -4.24818755

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.418479118, -4.24818755}

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