6x^2+5x-3=

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Solution for 6x^2+5x-3= equation:


Simplifying
6x2 + 5x + -3 = 0

Reorder the terms:
-3 + 5x + 6x2 = 0

Solving
-3 + 5x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-0.5 + 0.8333333333x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 0.8333333333x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 0.8333333333x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 0.8333333333x + x2 = 0 + 0.5
0.8333333333x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
0.8333333333x + x2 = 0.5

The x term is 0.8333333333x.  Take half its coefficient (0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
0.8333333333x + 0.1736111111 + x2 = 0.5 + 0.1736111111

Reorder the terms:
0.1736111111 + 0.8333333333x + x2 = 0.5 + 0.1736111111

Combine like terms: 0.5 + 0.1736111111 = 0.6736111111
0.1736111111 + 0.8333333333x + x2 = 0.6736111111

Factor a perfect square on the left side:
(x + 0.4166666667)(x + 0.4166666667) = 0.6736111111

Calculate the square root of the right side: 0.82073815

Break this problem into two subproblems by setting 
(x + 0.4166666667) equal to 0.82073815 and -0.82073815.

Subproblem 1

x + 0.4166666667 = 0.82073815 Simplifying x + 0.4166666667 = 0.82073815 Reorder the terms: 0.4166666667 + x = 0.82073815 Solving 0.4166666667 + x = 0.82073815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = 0.82073815 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = 0.82073815 + -0.4166666667 x = 0.82073815 + -0.4166666667 Combine like terms: 0.82073815 + -0.4166666667 = 0.4040714833 x = 0.4040714833 Simplifying x = 0.4040714833

Subproblem 2

x + 0.4166666667 = -0.82073815 Simplifying x + 0.4166666667 = -0.82073815 Reorder the terms: 0.4166666667 + x = -0.82073815 Solving 0.4166666667 + x = -0.82073815 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4166666667' to each side of the equation. 0.4166666667 + -0.4166666667 + x = -0.82073815 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + x = -0.82073815 + -0.4166666667 x = -0.82073815 + -0.4166666667 Combine like terms: -0.82073815 + -0.4166666667 = -1.2374048167 x = -1.2374048167 Simplifying x = -1.2374048167

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.4040714833, -1.2374048167}

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