16x^2-57x+49=0

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Solution for 16x^2-57x+49=0 equation:


Simplifying
16x2 + -57x + 49 = 0

Reorder the terms:
49 + -57x + 16x2 = 0

Solving
49 + -57x + 16x2 = 0

Solving for variable 'x'.

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

Divide each side by '16'.
3.0625 + -3.5625x + x2 = 0

Move the constant term to the right:

Add '-3.0625' to each side of the equation.
3.0625 + -3.5625x + -3.0625 + x2 = 0 + -3.0625

Reorder the terms:
3.0625 + -3.0625 + -3.5625x + x2 = 0 + -3.0625

Combine like terms: 3.0625 + -3.0625 = 0.0000
0.0000 + -3.5625x + x2 = 0 + -3.0625
-3.5625x + x2 = 0 + -3.0625

Combine like terms: 0 + -3.0625 = -3.0625
-3.5625x + x2 = -3.0625

The x term is -3.5625x.  Take half its coefficient (-1.78125).
Square it (3.172851563) and add it to both sides.

Add '3.172851563' to each side of the equation.
-3.5625x + 3.172851563 + x2 = -3.0625 + 3.172851563

Reorder the terms:
3.172851563 + -3.5625x + x2 = -3.0625 + 3.172851563

Combine like terms: -3.0625 + 3.172851563 = 0.110351563
3.172851563 + -3.5625x + x2 = 0.110351563

Factor a perfect square on the left side:
(x + -1.78125)(x + -1.78125) = 0.110351563

Calculate the square root of the right side: 0.332192057

Break this problem into two subproblems by setting 
(x + -1.78125) equal to 0.332192057 and -0.332192057.

Subproblem 1

x + -1.78125 = 0.332192057 Simplifying x + -1.78125 = 0.332192057 Reorder the terms: -1.78125 + x = 0.332192057 Solving -1.78125 + x = 0.332192057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.78125' to each side of the equation. -1.78125 + 1.78125 + x = 0.332192057 + 1.78125 Combine like terms: -1.78125 + 1.78125 = 0.00000 0.00000 + x = 0.332192057 + 1.78125 x = 0.332192057 + 1.78125 Combine like terms: 0.332192057 + 1.78125 = 2.113442057 x = 2.113442057 Simplifying x = 2.113442057

Subproblem 2

x + -1.78125 = -0.332192057 Simplifying x + -1.78125 = -0.332192057 Reorder the terms: -1.78125 + x = -0.332192057 Solving -1.78125 + x = -0.332192057 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.78125' to each side of the equation. -1.78125 + 1.78125 + x = -0.332192057 + 1.78125 Combine like terms: -1.78125 + 1.78125 = 0.00000 0.00000 + x = -0.332192057 + 1.78125 x = -0.332192057 + 1.78125 Combine like terms: -0.332192057 + 1.78125 = 1.449057943 x = 1.449057943 Simplifying x = 1.449057943

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.113442057, 1.449057943}

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