-9x^2+8x+3=0

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Solution for -9x^2+8x+3=0 equation:


Simplifying
-9x2 + 8x + 3 = 0

Reorder the terms:
3 + 8x + -9x2 = 0

Solving
3 + 8x + -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'.
-0.3333333333 + -0.8888888889x + x2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + -0.8888888889x + 0.3333333333 + x2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + -0.8888888889x + x2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + -0.8888888889x + x2 = 0 + 0.3333333333
-0.8888888889x + x2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
-0.8888888889x + x2 = 0.3333333333

The x term is -0.8888888889x.  Take half its coefficient (-0.4444444445).
Square it (0.1975308642) and add it to both sides.

Add '0.1975308642' to each side of the equation.
-0.8888888889x + 0.1975308642 + x2 = 0.3333333333 + 0.1975308642

Reorder the terms:
0.1975308642 + -0.8888888889x + x2 = 0.3333333333 + 0.1975308642

Combine like terms: 0.3333333333 + 0.1975308642 = 0.5308641975
0.1975308642 + -0.8888888889x + x2 = 0.5308641975

Factor a perfect square on the left side:
(x + -0.4444444445)(x + -0.4444444445) = 0.5308641975

Calculate the square root of the right side: 0.72860428

Break this problem into two subproblems by setting 
(x + -0.4444444445) equal to 0.72860428 and -0.72860428.

Subproblem 1

x + -0.4444444445 = 0.72860428 Simplifying x + -0.4444444445 = 0.72860428 Reorder the terms: -0.4444444445 + x = 0.72860428 Solving -0.4444444445 + x = 0.72860428 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + x = 0.72860428 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = 0.72860428 + 0.4444444445 x = 0.72860428 + 0.4444444445 Combine like terms: 0.72860428 + 0.4444444445 = 1.1730487245 x = 1.1730487245 Simplifying x = 1.1730487245

Subproblem 2

x + -0.4444444445 = -0.72860428 Simplifying x + -0.4444444445 = -0.72860428 Reorder the terms: -0.4444444445 + x = -0.72860428 Solving -0.4444444445 + x = -0.72860428 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + x = -0.72860428 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = -0.72860428 + 0.4444444445 x = -0.72860428 + 0.4444444445 Combine like terms: -0.72860428 + 0.4444444445 = -0.2841598355 x = -0.2841598355 Simplifying x = -0.2841598355

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.1730487245, -0.2841598355}

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