9x^2+12x-16=0

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Solution for 9x^2+12x-16=0 equation:


Simplifying
9x2 + 12x + -16 = 0

Reorder the terms:
-16 + 12x + 9x2 = 0

Solving
-16 + 12x + 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 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '1.777777778' to each side of the equation.
-1.777777778 + 1.333333333x + 1.777777778 + x2 = 0 + 1.777777778

Reorder the terms:
-1.777777778 + 1.777777778 + 1.333333333x + x2 = 0 + 1.777777778

Combine like terms: -1.777777778 + 1.777777778 = 0.000000000
0.000000000 + 1.333333333x + x2 = 0 + 1.777777778
1.333333333x + x2 = 0 + 1.777777778

Combine like terms: 0 + 1.777777778 = 1.777777778
1.333333333x + x2 = 1.777777778

The x term is 1.333333333x.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333x + 0.4444444442 + x2 = 1.777777778 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 1.777777778 + 0.4444444442

Combine like terms: 1.777777778 + 0.4444444442 = 2.2222222222
0.4444444442 + 1.333333333x + x2 = 2.2222222222

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 2.2222222222

Calculate the square root of the right side: 1.490711985

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 1.490711985 and -1.490711985.

Subproblem 1

x + 0.6666666665 = 1.490711985 Simplifying x + 0.6666666665 = 1.490711985 Reorder the terms: 0.6666666665 + x = 1.490711985 Solving 0.6666666665 + x = 1.490711985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 1.490711985 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 1.490711985 + -0.6666666665 x = 1.490711985 + -0.6666666665 Combine like terms: 1.490711985 + -0.6666666665 = 0.8240453185 x = 0.8240453185 Simplifying x = 0.8240453185

Subproblem 2

x + 0.6666666665 = -1.490711985 Simplifying x + 0.6666666665 = -1.490711985 Reorder the terms: 0.6666666665 + x = -1.490711985 Solving 0.6666666665 + x = -1.490711985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -1.490711985 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -1.490711985 + -0.6666666665 x = -1.490711985 + -0.6666666665 Combine like terms: -1.490711985 + -0.6666666665 = -2.1573786515 x = -2.1573786515 Simplifying x = -2.1573786515

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.8240453185, -2.1573786515}

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