35x^2=5x+8

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Solution for 35x^2=5x+8 equation:


Simplifying
35x2 = 5x + 8

Reorder the terms:
35x2 = 8 + 5x

Solving
35x2 = 8 + 5x

Solving for variable 'x'.

Reorder the terms:
-8 + -5x + 35x2 = 8 + 5x + -8 + -5x

Reorder the terms:
-8 + -5x + 35x2 = 8 + -8 + 5x + -5x

Combine like terms: 8 + -8 = 0
-8 + -5x + 35x2 = 0 + 5x + -5x
-8 + -5x + 35x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-8 + -5x + 35x2 = 0

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

Divide each side by '35'.
-0.2285714286 + -0.1428571429x + x2 = 0

Move the constant term to the right:

Add '0.2285714286' to each side of the equation.
-0.2285714286 + -0.1428571429x + 0.2285714286 + x2 = 0 + 0.2285714286

Reorder the terms:
-0.2285714286 + 0.2285714286 + -0.1428571429x + x2 = 0 + 0.2285714286

Combine like terms: -0.2285714286 + 0.2285714286 = 0.0000000000
0.0000000000 + -0.1428571429x + x2 = 0 + 0.2285714286
-0.1428571429x + x2 = 0 + 0.2285714286

Combine like terms: 0 + 0.2285714286 = 0.2285714286
-0.1428571429x + x2 = 0.2285714286

The x term is -0.1428571429x.  Take half its coefficient (-0.07142857145).
Square it (0.005102040819) and add it to both sides.

Add '0.005102040819' to each side of the equation.
-0.1428571429x + 0.005102040819 + x2 = 0.2285714286 + 0.005102040819

Reorder the terms:
0.005102040819 + -0.1428571429x + x2 = 0.2285714286 + 0.005102040819

Combine like terms: 0.2285714286 + 0.005102040819 = 0.233673469419
0.005102040819 + -0.1428571429x + x2 = 0.233673469419

Factor a perfect square on the left side:
(x + -0.07142857145)(x + -0.07142857145) = 0.233673469419

Calculate the square root of the right side: 0.483397838

Break this problem into two subproblems by setting 
(x + -0.07142857145) equal to 0.483397838 and -0.483397838.

Subproblem 1

x + -0.07142857145 = 0.483397838 Simplifying x + -0.07142857145 = 0.483397838 Reorder the terms: -0.07142857145 + x = 0.483397838 Solving -0.07142857145 + x = 0.483397838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = 0.483397838 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = 0.483397838 + 0.07142857145 x = 0.483397838 + 0.07142857145 Combine like terms: 0.483397838 + 0.07142857145 = 0.55482640945 x = 0.55482640945 Simplifying x = 0.55482640945

Subproblem 2

x + -0.07142857145 = -0.483397838 Simplifying x + -0.07142857145 = -0.483397838 Reorder the terms: -0.07142857145 + x = -0.483397838 Solving -0.07142857145 + x = -0.483397838 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.07142857145' to each side of the equation. -0.07142857145 + 0.07142857145 + x = -0.483397838 + 0.07142857145 Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000 0.00000000000 + x = -0.483397838 + 0.07142857145 x = -0.483397838 + 0.07142857145 Combine like terms: -0.483397838 + 0.07142857145 = -0.41196926655 x = -0.41196926655 Simplifying x = -0.41196926655

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.55482640945, -0.41196926655}

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