16x^2-49x+7=0

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Solution for 16x^2-49x+7=0 equation:


Simplifying
16x2 + -49x + 7 = 0

Reorder the terms:
7 + -49x + 16x2 = 0

Solving
7 + -49x + 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'.
0.4375 + -3.0625x + x2 = 0

Move the constant term to the right:

Add '-0.4375' to each side of the equation.
0.4375 + -3.0625x + -0.4375 + x2 = 0 + -0.4375

Reorder the terms:
0.4375 + -0.4375 + -3.0625x + x2 = 0 + -0.4375

Combine like terms: 0.4375 + -0.4375 = 0.0000
0.0000 + -3.0625x + x2 = 0 + -0.4375
-3.0625x + x2 = 0 + -0.4375

Combine like terms: 0 + -0.4375 = -0.4375
-3.0625x + x2 = -0.4375

The x term is -3.0625x.  Take half its coefficient (-1.53125).
Square it (2.344726563) and add it to both sides.

Add '2.344726563' to each side of the equation.
-3.0625x + 2.344726563 + x2 = -0.4375 + 2.344726563

Reorder the terms:
2.344726563 + -3.0625x + x2 = -0.4375 + 2.344726563

Combine like terms: -0.4375 + 2.344726563 = 1.907226563
2.344726563 + -3.0625x + x2 = 1.907226563

Factor a perfect square on the left side:
(x + -1.53125)(x + -1.53125) = 1.907226563

Calculate the square root of the right side: 1.381023737

Break this problem into two subproblems by setting 
(x + -1.53125) equal to 1.381023737 and -1.381023737.

Subproblem 1

x + -1.53125 = 1.381023737 Simplifying x + -1.53125 = 1.381023737 Reorder the terms: -1.53125 + x = 1.381023737 Solving -1.53125 + x = 1.381023737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.53125' to each side of the equation. -1.53125 + 1.53125 + x = 1.381023737 + 1.53125 Combine like terms: -1.53125 + 1.53125 = 0.00000 0.00000 + x = 1.381023737 + 1.53125 x = 1.381023737 + 1.53125 Combine like terms: 1.381023737 + 1.53125 = 2.912273737 x = 2.912273737 Simplifying x = 2.912273737

Subproblem 2

x + -1.53125 = -1.381023737 Simplifying x + -1.53125 = -1.381023737 Reorder the terms: -1.53125 + x = -1.381023737 Solving -1.53125 + x = -1.381023737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.53125' to each side of the equation. -1.53125 + 1.53125 + x = -1.381023737 + 1.53125 Combine like terms: -1.53125 + 1.53125 = 0.00000 0.00000 + x = -1.381023737 + 1.53125 x = -1.381023737 + 1.53125 Combine like terms: -1.381023737 + 1.53125 = 0.150226263 x = 0.150226263 Simplifying x = 0.150226263

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.912273737, 0.150226263}

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