7x^2+10x=5

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Solution for 7x^2+10x=5 equation:


Simplifying
7x2 + 10x = 5

Reorder the terms:
10x + 7x2 = 5

Solving
10x + 7x2 = 5

Solving for variable 'x'.

Reorder the terms:
-5 + 10x + 7x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 10x + 7x2 = 0

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

Divide each side by '7'.
-0.7142857143 + 1.428571429x + x2 = 0

Move the constant term to the right:

Add '0.7142857143' to each side of the equation.
-0.7142857143 + 1.428571429x + 0.7142857143 + x2 = 0 + 0.7142857143

Reorder the terms:
-0.7142857143 + 0.7142857143 + 1.428571429x + x2 = 0 + 0.7142857143

Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000
0.0000000000 + 1.428571429x + x2 = 0 + 0.7142857143
1.428571429x + x2 = 0 + 0.7142857143

Combine like terms: 0 + 0.7142857143 = 0.7142857143
1.428571429x + x2 = 0.7142857143

The x term is 1.428571429x.  Take half its coefficient (0.7142857145).
Square it (0.5102040819) and add it to both sides.

Add '0.5102040819' to each side of the equation.
1.428571429x + 0.5102040819 + x2 = 0.7142857143 + 0.5102040819

Reorder the terms:
0.5102040819 + 1.428571429x + x2 = 0.7142857143 + 0.5102040819

Combine like terms: 0.7142857143 + 0.5102040819 = 1.2244897962
0.5102040819 + 1.428571429x + x2 = 1.2244897962

Factor a perfect square on the left side:
(x + 0.7142857145)(x + 0.7142857145) = 1.2244897962

Calculate the square root of the right side: 1.10656667

Break this problem into two subproblems by setting 
(x + 0.7142857145) equal to 1.10656667 and -1.10656667.

Subproblem 1

x + 0.7142857145 = 1.10656667 Simplifying x + 0.7142857145 = 1.10656667 Reorder the terms: 0.7142857145 + x = 1.10656667 Solving 0.7142857145 + x = 1.10656667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + x = 1.10656667 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = 1.10656667 + -0.7142857145 x = 1.10656667 + -0.7142857145 Combine like terms: 1.10656667 + -0.7142857145 = 0.3922809555 x = 0.3922809555 Simplifying x = 0.3922809555

Subproblem 2

x + 0.7142857145 = -1.10656667 Simplifying x + 0.7142857145 = -1.10656667 Reorder the terms: 0.7142857145 + x = -1.10656667 Solving 0.7142857145 + x = -1.10656667 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + x = -1.10656667 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = -1.10656667 + -0.7142857145 x = -1.10656667 + -0.7142857145 Combine like terms: -1.10656667 + -0.7142857145 = -1.8208523845 x = -1.8208523845 Simplifying x = -1.8208523845

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.3922809555, -1.8208523845}

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