6x^2+10x-13=0

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Solution for 6x^2+10x-13=0 equation:


Simplifying
6x2 + 10x + -13 = 0

Reorder the terms:
-13 + 10x + 6x2 = 0

Solving
-13 + 10x + 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'.
-2.166666667 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '2.166666667' to each side of the equation.
-2.166666667 + 1.666666667x + 2.166666667 + x2 = 0 + 2.166666667

Reorder the terms:
-2.166666667 + 2.166666667 + 1.666666667x + x2 = 0 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + 1.666666667x + x2 = 0 + 2.166666667
1.666666667x + x2 = 0 + 2.166666667

Combine like terms: 0 + 2.166666667 = 2.166666667
1.666666667x + x2 = 2.166666667

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 2.166666667 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 2.166666667 + 0.6944444447

Combine like terms: 2.166666667 + 0.6944444447 = 2.8611111117
0.6944444447 + 1.666666667x + x2 = 2.8611111117

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 2.8611111117

Calculate the square root of the right side: 1.691481928

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 1.691481928 and -1.691481928.

Subproblem 1

x + 0.8333333335 = 1.691481928 Simplifying x + 0.8333333335 = 1.691481928 Reorder the terms: 0.8333333335 + x = 1.691481928 Solving 0.8333333335 + x = 1.691481928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = 1.691481928 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 1.691481928 + -0.8333333335 x = 1.691481928 + -0.8333333335 Combine like terms: 1.691481928 + -0.8333333335 = 0.8581485945 x = 0.8581485945 Simplifying x = 0.8581485945

Subproblem 2

x + 0.8333333335 = -1.691481928 Simplifying x + 0.8333333335 = -1.691481928 Reorder the terms: 0.8333333335 + x = -1.691481928 Solving 0.8333333335 + x = -1.691481928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8333333335' to each side of the equation. 0.8333333335 + -0.8333333335 + x = -1.691481928 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -1.691481928 + -0.8333333335 x = -1.691481928 + -0.8333333335 Combine like terms: -1.691481928 + -0.8333333335 = -2.5248152615 x = -2.5248152615 Simplifying x = -2.5248152615

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.8581485945, -2.5248152615}

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