14x^2=x+35

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Solution for 14x^2=x+35 equation:


Simplifying
14x2 = x + 35

Reorder the terms:
14x2 = 35 + x

Solving
14x2 = 35 + x

Solving for variable 'x'.

Reorder the terms:
-35 + -1x + 14x2 = 35 + x + -35 + -1x

Reorder the terms:
-35 + -1x + 14x2 = 35 + -35 + x + -1x

Combine like terms: 35 + -35 = 0
-35 + -1x + 14x2 = 0 + x + -1x
-35 + -1x + 14x2 = x + -1x

Combine like terms: x + -1x = 0
-35 + -1x + 14x2 = 0

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

Divide each side by '14'.
-2.5 + -0.07142857143x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -0.07142857143x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -0.07142857143x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -0.07142857143x + x2 = 0 + 2.5
-0.07142857143x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-0.07142857143x + x2 = 2.5

The x term is -0.07142857143x.  Take half its coefficient (-0.03571428572).
Square it (0.001275510204) and add it to both sides.

Add '0.001275510204' to each side of the equation.
-0.07142857143x + 0.001275510204 + x2 = 2.5 + 0.001275510204

Reorder the terms:
0.001275510204 + -0.07142857143x + x2 = 2.5 + 0.001275510204

Combine like terms: 2.5 + 0.001275510204 = 2.501275510204
0.001275510204 + -0.07142857143x + x2 = 2.501275510204

Factor a perfect square on the left side:
(x + -0.03571428572)(x + -0.03571428572) = 2.501275510204

Calculate the square root of the right side: 1.58154213

Break this problem into two subproblems by setting 
(x + -0.03571428572) equal to 1.58154213 and -1.58154213.

Subproblem 1

x + -0.03571428572 = 1.58154213 Simplifying x + -0.03571428572 = 1.58154213 Reorder the terms: -0.03571428572 + x = 1.58154213 Solving -0.03571428572 + x = 1.58154213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03571428572' to each side of the equation. -0.03571428572 + 0.03571428572 + x = 1.58154213 + 0.03571428572 Combine like terms: -0.03571428572 + 0.03571428572 = 0.00000000000 0.00000000000 + x = 1.58154213 + 0.03571428572 x = 1.58154213 + 0.03571428572 Combine like terms: 1.58154213 + 0.03571428572 = 1.61725641572 x = 1.61725641572 Simplifying x = 1.61725641572

Subproblem 2

x + -0.03571428572 = -1.58154213 Simplifying x + -0.03571428572 = -1.58154213 Reorder the terms: -0.03571428572 + x = -1.58154213 Solving -0.03571428572 + x = -1.58154213 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03571428572' to each side of the equation. -0.03571428572 + 0.03571428572 + x = -1.58154213 + 0.03571428572 Combine like terms: -0.03571428572 + 0.03571428572 = 0.00000000000 0.00000000000 + x = -1.58154213 + 0.03571428572 x = -1.58154213 + 0.03571428572 Combine like terms: -1.58154213 + 0.03571428572 = -1.54582784428 x = -1.54582784428 Simplifying x = -1.54582784428

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.61725641572, -1.54582784428}

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