-9x^2+14x-4=0

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Solution for -9x^2+14x-4=0 equation:


Simplifying
-9x2 + 14x + -4 = 0

Reorder the terms:
-4 + 14x + -9x2 = 0

Solving
-4 + 14x + -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'.
0.4444444444 + -1.555555556x + x2 = 0

Move the constant term to the right:

Add '-0.4444444444' to each side of the equation.
0.4444444444 + -1.555555556x + -0.4444444444 + x2 = 0 + -0.4444444444

Reorder the terms:
0.4444444444 + -0.4444444444 + -1.555555556x + x2 = 0 + -0.4444444444

Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000
0.0000000000 + -1.555555556x + x2 = 0 + -0.4444444444
-1.555555556x + x2 = 0 + -0.4444444444

Combine like terms: 0 + -0.4444444444 = -0.4444444444
-1.555555556x + x2 = -0.4444444444

The x term is -1.555555556x.  Take half its coefficient (-0.777777778).
Square it (0.6049382720) and add it to both sides.

Add '0.6049382720' to each side of the equation.
-1.555555556x + 0.6049382720 + x2 = -0.4444444444 + 0.6049382720

Reorder the terms:
0.6049382720 + -1.555555556x + x2 = -0.4444444444 + 0.6049382720

Combine like terms: -0.4444444444 + 0.6049382720 = 0.1604938276
0.6049382720 + -1.555555556x + x2 = 0.1604938276

Factor a perfect square on the left side:
(x + -0.777777778)(x + -0.777777778) = 0.1604938276

Calculate the square root of the right side: 0.400616809

Break this problem into two subproblems by setting 
(x + -0.777777778) equal to 0.400616809 and -0.400616809.

Subproblem 1

x + -0.777777778 = 0.400616809 Simplifying x + -0.777777778 = 0.400616809 Reorder the terms: -0.777777778 + x = 0.400616809 Solving -0.777777778 + x = 0.400616809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.777777778' to each side of the equation. -0.777777778 + 0.777777778 + x = 0.400616809 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + x = 0.400616809 + 0.777777778 x = 0.400616809 + 0.777777778 Combine like terms: 0.400616809 + 0.777777778 = 1.178394587 x = 1.178394587 Simplifying x = 1.178394587

Subproblem 2

x + -0.777777778 = -0.400616809 Simplifying x + -0.777777778 = -0.400616809 Reorder the terms: -0.777777778 + x = -0.400616809 Solving -0.777777778 + x = -0.400616809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.777777778' to each side of the equation. -0.777777778 + 0.777777778 + x = -0.400616809 + 0.777777778 Combine like terms: -0.777777778 + 0.777777778 = 0.000000000 0.000000000 + x = -0.400616809 + 0.777777778 x = -0.400616809 + 0.777777778 Combine like terms: -0.400616809 + 0.777777778 = 0.377160969 x = 0.377160969 Simplifying x = 0.377160969

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.178394587, 0.377160969}

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