9x^2-12x+4=87

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Solution for 9x^2-12x+4=87 equation:


Simplifying
9x2 + -12x + 4 = 87

Reorder the terms:
4 + -12x + 9x2 = 87

Solving
4 + -12x + 9x2 = 87

Solving for variable 'x'.

Reorder the terms:
4 + -87 + -12x + 9x2 = 87 + -87

Combine like terms: 4 + -87 = -83
-83 + -12x + 9x2 = 87 + -87

Combine like terms: 87 + -87 = 0
-83 + -12x + 9x2 = 0

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

Divide each side by '9'.
-9.222222222 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '9.222222222' to each side of the equation.
-9.222222222 + -1.333333333x + 9.222222222 + x2 = 0 + 9.222222222

Reorder the terms:
-9.222222222 + 9.222222222 + -1.333333333x + x2 = 0 + 9.222222222

Combine like terms: -9.222222222 + 9.222222222 = 0.000000000
0.000000000 + -1.333333333x + x2 = 0 + 9.222222222
-1.333333333x + x2 = 0 + 9.222222222

Combine like terms: 0 + 9.222222222 = 9.222222222
-1.333333333x + x2 = 9.222222222

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 = 9.222222222 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 9.222222222 + 0.4444444442

Combine like terms: 9.222222222 + 0.4444444442 = 9.6666666662
0.4444444442 + -1.333333333x + x2 = 9.6666666662

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 9.6666666662

Calculate the square root of the right side: 3.109126351

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 3.109126351 and -3.109126351.

Subproblem 1

x + -0.6666666665 = 3.109126351 Simplifying x + -0.6666666665 = 3.109126351 Reorder the terms: -0.6666666665 + x = 3.109126351 Solving -0.6666666665 + x = 3.109126351 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 = 3.109126351 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 3.109126351 + 0.6666666665 x = 3.109126351 + 0.6666666665 Combine like terms: 3.109126351 + 0.6666666665 = 3.7757930175 x = 3.7757930175 Simplifying x = 3.7757930175

Subproblem 2

x + -0.6666666665 = -3.109126351 Simplifying x + -0.6666666665 = -3.109126351 Reorder the terms: -0.6666666665 + x = -3.109126351 Solving -0.6666666665 + x = -3.109126351 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 = -3.109126351 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -3.109126351 + 0.6666666665 x = -3.109126351 + 0.6666666665 Combine like terms: -3.109126351 + 0.6666666665 = -2.4424596845 x = -2.4424596845 Simplifying x = -2.4424596845

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.7757930175, -2.4424596845}

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