7x^2-13x-35=0

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Solution for 7x^2-13x-35=0 equation:


Simplifying
7x2 + -13x + -35 = 0

Reorder the terms:
-35 + -13x + 7x2 = 0

Solving
-35 + -13x + 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'.
-5 + -1.857142857x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -1.857142857x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -1.857142857x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1.857142857x + x2 = 0 + 5
-1.857142857x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-1.857142857x + x2 = 5

The x term is -1.857142857x.  Take half its coefficient (-0.9285714285).
Square it (0.8622448978) and add it to both sides.

Add '0.8622448978' to each side of the equation.
-1.857142857x + 0.8622448978 + x2 = 5 + 0.8622448978

Reorder the terms:
0.8622448978 + -1.857142857x + x2 = 5 + 0.8622448978

Combine like terms: 5 + 0.8622448978 = 5.8622448978
0.8622448978 + -1.857142857x + x2 = 5.8622448978

Factor a perfect square on the left side:
(x + -0.9285714285)(x + -0.9285714285) = 5.8622448978

Calculate the square root of the right side: 2.421207322

Break this problem into two subproblems by setting 
(x + -0.9285714285) equal to 2.421207322 and -2.421207322.

Subproblem 1

x + -0.9285714285 = 2.421207322 Simplifying x + -0.9285714285 = 2.421207322 Reorder the terms: -0.9285714285 + x = 2.421207322 Solving -0.9285714285 + x = 2.421207322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9285714285' to each side of the equation. -0.9285714285 + 0.9285714285 + x = 2.421207322 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + x = 2.421207322 + 0.9285714285 x = 2.421207322 + 0.9285714285 Combine like terms: 2.421207322 + 0.9285714285 = 3.3497787505 x = 3.3497787505 Simplifying x = 3.3497787505

Subproblem 2

x + -0.9285714285 = -2.421207322 Simplifying x + -0.9285714285 = -2.421207322 Reorder the terms: -0.9285714285 + x = -2.421207322 Solving -0.9285714285 + x = -2.421207322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9285714285' to each side of the equation. -0.9285714285 + 0.9285714285 + x = -2.421207322 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + x = -2.421207322 + 0.9285714285 x = -2.421207322 + 0.9285714285 Combine like terms: -2.421207322 + 0.9285714285 = -1.4926358935 x = -1.4926358935 Simplifying x = -1.4926358935

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.3497787505, -1.4926358935}

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