0=9x^2-49x+64

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Solution for 0=9x^2-49x+64 equation:


Simplifying
0 = 9x2 + -49x + 64

Reorder the terms:
0 = 64 + -49x + 9x2

Solving
0 = 64 + -49x + 9x2

Solving for variable 'x'.

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

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

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

Combine like terms: -49x + 49x = 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 = 0.299382715
7.410493826 + -5.444444444x + x2 = 0.299382715

Factor a perfect square on the left side:
(x + -2.722222222)(x + -2.722222222) = 0.299382715

Calculate the square root of the right side: 0.547158766

Break this problem into two subproblems by setting 
(x + -2.722222222) equal to 0.547158766 and -0.547158766.

Subproblem 1

x + -2.722222222 = 0.547158766 Simplifying x + -2.722222222 = 0.547158766 Reorder the terms: -2.722222222 + x = 0.547158766 Solving -2.722222222 + x = 0.547158766 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 = 0.547158766 + 2.722222222 Combine like terms: -2.722222222 + 2.722222222 = 0.000000000 0.000000000 + x = 0.547158766 + 2.722222222 x = 0.547158766 + 2.722222222 Combine like terms: 0.547158766 + 2.722222222 = 3.269380988 x = 3.269380988 Simplifying x = 3.269380988

Subproblem 2

x + -2.722222222 = -0.547158766 Simplifying x + -2.722222222 = -0.547158766 Reorder the terms: -2.722222222 + x = -0.547158766 Solving -2.722222222 + x = -0.547158766 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 = -0.547158766 + 2.722222222 Combine like terms: -2.722222222 + 2.722222222 = 0.000000000 0.000000000 + x = -0.547158766 + 2.722222222 x = -0.547158766 + 2.722222222 Combine like terms: -0.547158766 + 2.722222222 = 2.175063456 x = 2.175063456 Simplifying x = 2.175063456

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.269380988, 2.175063456}

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