7x^2-35x+16=0

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Solution for 7x^2-35x+16=0 equation:


Simplifying
7x2 + -35x + 16 = 0

Reorder the terms:
16 + -35x + 7x2 = 0

Solving
16 + -35x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
2.285714286 + -5x + x2 = 0

Move the constant term to the right:

Add '-2.285714286' to each side of the equation.
2.285714286 + -5x + -2.285714286 + x2 = 0 + -2.285714286

Reorder the terms:
2.285714286 + -2.285714286 + -5x + x2 = 0 + -2.285714286

Combine like terms: 2.285714286 + -2.285714286 = 0.000000000
0.000000000 + -5x + x2 = 0 + -2.285714286
-5x + x2 = 0 + -2.285714286

Combine like terms: 0 + -2.285714286 = -2.285714286
-5x + x2 = -2.285714286

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -2.285714286 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -2.285714286 + 6.25

Combine like terms: -2.285714286 + 6.25 = 3.964285714
6.25 + -5x + x2 = 3.964285714

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 3.964285714

Calculate the square root of the right side: 1.991051409

Break this problem into two subproblems by setting 
(x + -2.5) equal to 1.991051409 and -1.991051409.

Subproblem 1

x + -2.5 = 1.991051409 Simplifying x + -2.5 = 1.991051409 Reorder the terms: -2.5 + x = 1.991051409 Solving -2.5 + x = 1.991051409 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 1.991051409 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.991051409 + 2.5 x = 1.991051409 + 2.5 Combine like terms: 1.991051409 + 2.5 = 4.491051409 x = 4.491051409 Simplifying x = 4.491051409

Subproblem 2

x + -2.5 = -1.991051409 Simplifying x + -2.5 = -1.991051409 Reorder the terms: -2.5 + x = -1.991051409 Solving -2.5 + x = -1.991051409 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -1.991051409 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.991051409 + 2.5 x = -1.991051409 + 2.5 Combine like terms: -1.991051409 + 2.5 = 0.508948591 x = 0.508948591 Simplifying x = 0.508948591

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.491051409, 0.508948591}

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