0=-9X^2+7X+4

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Solution for 0=-9X^2+7X+4 equation:


Simplifying
0 = -9X2 + 7X + 4

Reorder the terms:
0 = 4 + 7X + -9X2

Solving
0 = 4 + 7X + -9X2

Solving for variable 'X'.

Combine like terms: 0 + -4 = -4
-4 + -7X + 9X2 = 4 + 7X + -9X2 + -4 + -7X + 9X2

Reorder the terms:
-4 + -7X + 9X2 = 4 + -4 + 7X + -7X + -9X2 + 9X2

Combine like terms: 4 + -4 = 0
-4 + -7X + 9X2 = 0 + 7X + -7X + -9X2 + 9X2
-4 + -7X + 9X2 = 7X + -7X + -9X2 + 9X2

Combine like terms: 7X + -7X = 0
-4 + -7X + 9X2 = 0 + -9X2 + 9X2
-4 + -7X + 9X2 = -9X2 + 9X2

Combine like terms: -9X2 + 9X2 = 0
-4 + -7X + 9X2 = 0

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

Divide each side by '9'.
-0.4444444444 + -0.7777777778X + X2 = 0

Move the constant term to the right:

Add '0.4444444444' to each side of the equation.
-0.4444444444 + -0.7777777778X + 0.4444444444 + X2 = 0 + 0.4444444444

Reorder the terms:
-0.4444444444 + 0.4444444444 + -0.7777777778X + X2 = 0 + 0.4444444444

Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000
0.0000000000 + -0.7777777778X + X2 = 0 + 0.4444444444
-0.7777777778X + X2 = 0 + 0.4444444444

Combine like terms: 0 + 0.4444444444 = 0.4444444444
-0.7777777778X + X2 = 0.4444444444

The X term is -0.7777777778X.  Take half its coefficient (-0.3888888889).
Square it (0.1512345679) and add it to both sides.

Add '0.1512345679' to each side of the equation.
-0.7777777778X + 0.1512345679 + X2 = 0.4444444444 + 0.1512345679

Reorder the terms:
0.1512345679 + -0.7777777778X + X2 = 0.4444444444 + 0.1512345679

Combine like terms: 0.4444444444 + 0.1512345679 = 0.5956790123
0.1512345679 + -0.7777777778X + X2 = 0.5956790123

Factor a perfect square on the left side:
(X + -0.3888888889)(X + -0.3888888889) = 0.5956790123

Calculate the square root of the right side: 0.771802444

Break this problem into two subproblems by setting 
(X + -0.3888888889) equal to 0.771802444 and -0.771802444.

Subproblem 1

X + -0.3888888889 = 0.771802444 Simplifying X + -0.3888888889 = 0.771802444 Reorder the terms: -0.3888888889 + X = 0.771802444 Solving -0.3888888889 + X = 0.771802444 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + X = 0.771802444 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + X = 0.771802444 + 0.3888888889 X = 0.771802444 + 0.3888888889 Combine like terms: 0.771802444 + 0.3888888889 = 1.1606913329 X = 1.1606913329 Simplifying X = 1.1606913329

Subproblem 2

X + -0.3888888889 = -0.771802444 Simplifying X + -0.3888888889 = -0.771802444 Reorder the terms: -0.3888888889 + X = -0.771802444 Solving -0.3888888889 + X = -0.771802444 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.3888888889' to each side of the equation. -0.3888888889 + 0.3888888889 + X = -0.771802444 + 0.3888888889 Combine like terms: -0.3888888889 + 0.3888888889 = 0.0000000000 0.0000000000 + X = -0.771802444 + 0.3888888889 X = -0.771802444 + 0.3888888889 Combine like terms: -0.771802444 + 0.3888888889 = -0.3829135551 X = -0.3829135551 Simplifying X = -0.3829135551

Solution

The solution to the problem is based on the solutions from the subproblems. X = {1.1606913329, -0.3829135551}

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