9x^2+7x-4=0

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


Simplifying
9x2 + 7x + -4 = 0

Reorder the terms:
-4 + 7x + 9x2 = 0

Solving
-4 + 7x + 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 + 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 = 0.3829135551 x = 0.3829135551 Simplifying x = 0.3829135551

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 = -1.1606913329 x = -1.1606913329 Simplifying x = -1.1606913329

Solution

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

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