x=9x^2-48x-64

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Solution for x=9x^2-48x-64 equation:


Simplifying
x = 9x2 + -48x + -64

Reorder the terms:
x = -64 + -48x + 9x2

Solving
x = -64 + -48x + 9x2

Solving for variable 'x'.

Reorder the terms:
64 + x + 48x + -9x2 = -64 + -48x + 9x2 + 64 + 48x + -9x2

Combine like terms: x + 48x = 49x
64 + 49x + -9x2 = -64 + -48x + 9x2 + 64 + 48x + -9x2

Reorder the terms:
64 + 49x + -9x2 = -64 + 64 + -48x + 48x + 9x2 + -9x2

Combine like terms: -64 + 64 = 0
64 + 49x + -9x2 = 0 + -48x + 48x + 9x2 + -9x2
64 + 49x + -9x2 = -48x + 48x + 9x2 + -9x2

Combine like terms: -48x + 48x = 0
64 + 49x + -9x2 = 0 + 9x2 + -9x2
64 + 49x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
64 + 49x + -9x2 = 0

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

Divide each side by '-9'.
-7.111111111 + -5.444444444x + x2 = 0

Move the constant term to the right:

Add '7.111111111' to each side of the equation.
-7.111111111 + -5.444444444x + 7.111111111 + x2 = 0 + 7.111111111

Reorder the terms:
-7.111111111 + 7.111111111 + -5.444444444x + x2 = 0 + 7.111111111

Combine like terms: -7.111111111 + 7.111111111 = 0.000000000
0.000000000 + -5.444444444x + x2 = 0 + 7.111111111
-5.444444444x + x2 = 0 + 7.111111111

Combine like terms: 0 + 7.111111111 = 7.111111111
-5.444444444x + x2 = 7.111111111

The x term is -5.444444444x.  Take half its coefficient (-2.722222222).
Square it (7.410493826) and add it to both sides.

Add '7.410493826' to each side of the equation.
-5.444444444x + 7.410493826 + x2 = 7.111111111 + 7.410493826

Reorder the terms:
7.410493826 + -5.444444444x + x2 = 7.111111111 + 7.410493826

Combine like terms: 7.111111111 + 7.410493826 = 14.521604937
7.410493826 + -5.444444444x + x2 = 14.521604937

Factor a perfect square on the left side:
(x + -2.722222222)(x + -2.722222222) = 14.521604937

Calculate the square root of the right side: 3.810722364

Break this problem into two subproblems by setting 
(x + -2.722222222) equal to 3.810722364 and -3.810722364.

Subproblem 1

x + -2.722222222 = 3.810722364 Simplifying x + -2.722222222 = 3.810722364 Reorder the terms: -2.722222222 + x = 3.810722364 Solving -2.722222222 + x = 3.810722364 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.722222222' to each side of the equation. -2.722222222 + 2.722222222 + x = 3.810722364 + 2.722222222 Combine like terms: -2.722222222 + 2.722222222 = 0.000000000 0.000000000 + x = 3.810722364 + 2.722222222 x = 3.810722364 + 2.722222222 Combine like terms: 3.810722364 + 2.722222222 = 6.532944586 x = 6.532944586 Simplifying x = 6.532944586

Subproblem 2

x + -2.722222222 = -3.810722364 Simplifying x + -2.722222222 = -3.810722364 Reorder the terms: -2.722222222 + x = -3.810722364 Solving -2.722222222 + x = -3.810722364 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.722222222' to each side of the equation. -2.722222222 + 2.722222222 + x = -3.810722364 + 2.722222222 Combine like terms: -2.722222222 + 2.722222222 = 0.000000000 0.000000000 + x = -3.810722364 + 2.722222222 x = -3.810722364 + 2.722222222 Combine like terms: -3.810722364 + 2.722222222 = -1.088500142 x = -1.088500142 Simplifying x = -1.088500142

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.532944586, -1.088500142}

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