9x^2-4x-63=0

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Solution for 9x^2-4x-63=0 equation:


Simplifying
9x2 + -4x + -63 = 0

Reorder the terms:
-63 + -4x + 9x2 = 0

Solving
-63 + -4x + 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'.
-7 + -0.4444444444x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -0.4444444444x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -0.4444444444x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -0.4444444444x + x2 = 0 + 7
-0.4444444444x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-0.4444444444x + x2 = 7

The x term is -0.4444444444x.  Take half its coefficient (-0.2222222222).
Square it (0.04938271604) and add it to both sides.

Add '0.04938271604' to each side of the equation.
-0.4444444444x + 0.04938271604 + x2 = 7 + 0.04938271604

Reorder the terms:
0.04938271604 + -0.4444444444x + x2 = 7 + 0.04938271604

Combine like terms: 7 + 0.04938271604 = 7.04938271604
0.04938271604 + -0.4444444444x + x2 = 7.04938271604

Factor a perfect square on the left side:
(x + -0.2222222222)(x + -0.2222222222) = 7.04938271604

Calculate the square root of the right side: 2.655067366

Break this problem into two subproblems by setting 
(x + -0.2222222222) equal to 2.655067366 and -2.655067366.

Subproblem 1

x + -0.2222222222 = 2.655067366 Simplifying x + -0.2222222222 = 2.655067366 Reorder the terms: -0.2222222222 + x = 2.655067366 Solving -0.2222222222 + x = 2.655067366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x = 2.655067366 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = 2.655067366 + 0.2222222222 x = 2.655067366 + 0.2222222222 Combine like terms: 2.655067366 + 0.2222222222 = 2.8772895882 x = 2.8772895882 Simplifying x = 2.8772895882

Subproblem 2

x + -0.2222222222 = -2.655067366 Simplifying x + -0.2222222222 = -2.655067366 Reorder the terms: -0.2222222222 + x = -2.655067366 Solving -0.2222222222 + x = -2.655067366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + x = -2.655067366 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + x = -2.655067366 + 0.2222222222 x = -2.655067366 + 0.2222222222 Combine like terms: -2.655067366 + 0.2222222222 = -2.4328451438 x = -2.4328451438 Simplifying x = -2.4328451438

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.8772895882, -2.4328451438}

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