7x^2+10x-6=

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Solution for 7x^2+10x-6= equation:


Simplifying
7x2 + 10x + -6 = 0

Reorder the terms:
-6 + 10x + 7x2 = 0

Solving
-6 + 10x + 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'.
-0.8571428571 + 1.428571429x + x2 = 0

Move the constant term to the right:

Add '0.8571428571' to each side of the equation.
-0.8571428571 + 1.428571429x + 0.8571428571 + x2 = 0 + 0.8571428571

Reorder the terms:
-0.8571428571 + 0.8571428571 + 1.428571429x + x2 = 0 + 0.8571428571

Combine like terms: -0.8571428571 + 0.8571428571 = 0.0000000000
0.0000000000 + 1.428571429x + x2 = 0 + 0.8571428571
1.428571429x + x2 = 0 + 0.8571428571

Combine like terms: 0 + 0.8571428571 = 0.8571428571
1.428571429x + x2 = 0.8571428571

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 = 0.8571428571 + 0.5102040819

Reorder the terms:
0.5102040819 + 1.428571429x + x2 = 0.8571428571 + 0.5102040819

Combine like terms: 0.8571428571 + 0.5102040819 = 1.367346939
0.5102040819 + 1.428571429x + x2 = 1.367346939

Factor a perfect square on the left side:
(x + 0.7142857145)(x + 0.7142857145) = 1.367346939

Calculate the square root of the right side: 1.16933611

Break this problem into two subproblems by setting 
(x + 0.7142857145) equal to 1.16933611 and -1.16933611.

Subproblem 1

x + 0.7142857145 = 1.16933611 Simplifying x + 0.7142857145 = 1.16933611 Reorder the terms: 0.7142857145 + x = 1.16933611 Solving 0.7142857145 + x = 1.16933611 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 = 1.16933611 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = 1.16933611 + -0.7142857145 x = 1.16933611 + -0.7142857145 Combine like terms: 1.16933611 + -0.7142857145 = 0.4550503955 x = 0.4550503955 Simplifying x = 0.4550503955

Subproblem 2

x + 0.7142857145 = -1.16933611 Simplifying x + 0.7142857145 = -1.16933611 Reorder the terms: 0.7142857145 + x = -1.16933611 Solving 0.7142857145 + x = -1.16933611 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 = -1.16933611 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = -1.16933611 + -0.7142857145 x = -1.16933611 + -0.7142857145 Combine like terms: -1.16933611 + -0.7142857145 = -1.8836218245 x = -1.8836218245 Simplifying x = -1.8836218245

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.4550503955, -1.8836218245}

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