7x^2+26x+12=0

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Solution for 7x^2+26x+12=0 equation:


Simplifying
7x2 + 26x + 12 = 0

Reorder the terms:
12 + 26x + 7x2 = 0

Solving
12 + 26x + 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'.
1.714285714 + 3.714285714x + x2 = 0

Move the constant term to the right:

Add '-1.714285714' to each side of the equation.
1.714285714 + 3.714285714x + -1.714285714 + x2 = 0 + -1.714285714

Reorder the terms:
1.714285714 + -1.714285714 + 3.714285714x + x2 = 0 + -1.714285714

Combine like terms: 1.714285714 + -1.714285714 = 0.000000000
0.000000000 + 3.714285714x + x2 = 0 + -1.714285714
3.714285714x + x2 = 0 + -1.714285714

Combine like terms: 0 + -1.714285714 = -1.714285714
3.714285714x + x2 = -1.714285714

The x term is 3.714285714x.  Take half its coefficient (1.857142857).
Square it (3.448979591) and add it to both sides.

Add '3.448979591' to each side of the equation.
3.714285714x + 3.448979591 + x2 = -1.714285714 + 3.448979591

Reorder the terms:
3.448979591 + 3.714285714x + x2 = -1.714285714 + 3.448979591

Combine like terms: -1.714285714 + 3.448979591 = 1.734693877
3.448979591 + 3.714285714x + x2 = 1.734693877

Factor a perfect square on the left side:
(x + 1.857142857)(x + 1.857142857) = 1.734693877

Calculate the square root of the right side: 1.317077779

Break this problem into two subproblems by setting 
(x + 1.857142857) equal to 1.317077779 and -1.317077779.

Subproblem 1

x + 1.857142857 = 1.317077779 Simplifying x + 1.857142857 = 1.317077779 Reorder the terms: 1.857142857 + x = 1.317077779 Solving 1.857142857 + x = 1.317077779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.857142857' to each side of the equation. 1.857142857 + -1.857142857 + x = 1.317077779 + -1.857142857 Combine like terms: 1.857142857 + -1.857142857 = 0.000000000 0.000000000 + x = 1.317077779 + -1.857142857 x = 1.317077779 + -1.857142857 Combine like terms: 1.317077779 + -1.857142857 = -0.540065078 x = -0.540065078 Simplifying x = -0.540065078

Subproblem 2

x + 1.857142857 = -1.317077779 Simplifying x + 1.857142857 = -1.317077779 Reorder the terms: 1.857142857 + x = -1.317077779 Solving 1.857142857 + x = -1.317077779 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.857142857' to each side of the equation. 1.857142857 + -1.857142857 + x = -1.317077779 + -1.857142857 Combine like terms: 1.857142857 + -1.857142857 = 0.000000000 0.000000000 + x = -1.317077779 + -1.857142857 x = -1.317077779 + -1.857142857 Combine like terms: -1.317077779 + -1.857142857 = -3.174220636 x = -3.174220636 Simplifying x = -3.174220636

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.540065078, -3.174220636}

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