7x^2-13x=5

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Solution for 7x^2-13x=5 equation:


Simplifying
7x2 + -13x = 5

Reorder the terms:
-13x + 7x2 = 5

Solving
-13x + 7x2 = 5

Solving for variable 'x'.

Reorder the terms:
-5 + -13x + 7x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -13x + 7x2 = 0

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

Divide each side by '7'.
-0.7142857143 + -1.857142857x + x2 = 0

Move the constant term to the right:

Add '0.7142857143' to each side of the equation.
-0.7142857143 + -1.857142857x + 0.7142857143 + x2 = 0 + 0.7142857143

Reorder the terms:
-0.7142857143 + 0.7142857143 + -1.857142857x + x2 = 0 + 0.7142857143

Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000
0.0000000000 + -1.857142857x + x2 = 0 + 0.7142857143
-1.857142857x + x2 = 0 + 0.7142857143

Combine like terms: 0 + 0.7142857143 = 0.7142857143
-1.857142857x + x2 = 0.7142857143

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 = 0.7142857143 + 0.8622448978

Reorder the terms:
0.8622448978 + -1.857142857x + x2 = 0.7142857143 + 0.8622448978

Combine like terms: 0.7142857143 + 0.8622448978 = 1.5765306121
0.8622448978 + -1.857142857x + x2 = 1.5765306121

Factor a perfect square on the left side:
(x + -0.9285714285)(x + -0.9285714285) = 1.5765306121

Calculate the square root of the right side: 1.255599702

Break this problem into two subproblems by setting 
(x + -0.9285714285) equal to 1.255599702 and -1.255599702.

Subproblem 1

x + -0.9285714285 = 1.255599702 Simplifying x + -0.9285714285 = 1.255599702 Reorder the terms: -0.9285714285 + x = 1.255599702 Solving -0.9285714285 + x = 1.255599702 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 = 1.255599702 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + x = 1.255599702 + 0.9285714285 x = 1.255599702 + 0.9285714285 Combine like terms: 1.255599702 + 0.9285714285 = 2.1841711305 x = 2.1841711305 Simplifying x = 2.1841711305

Subproblem 2

x + -0.9285714285 = -1.255599702 Simplifying x + -0.9285714285 = -1.255599702 Reorder the terms: -0.9285714285 + x = -1.255599702 Solving -0.9285714285 + x = -1.255599702 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 = -1.255599702 + 0.9285714285 Combine like terms: -0.9285714285 + 0.9285714285 = 0.0000000000 0.0000000000 + x = -1.255599702 + 0.9285714285 x = -1.255599702 + 0.9285714285 Combine like terms: -1.255599702 + 0.9285714285 = -0.3270282735 x = -0.3270282735 Simplifying x = -0.3270282735

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.1841711305, -0.3270282735}

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