6x^2+15x-37=0

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Solution for 6x^2+15x-37=0 equation:


Simplifying
6x2 + 15x + -37 = 0

Reorder the terms:
-37 + 15x + 6x2 = 0

Solving
-37 + 15x + 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'.
-6.166666667 + 2.5x + x2 = 0

Move the constant term to the right:

Add '6.166666667' to each side of the equation.
-6.166666667 + 2.5x + 6.166666667 + x2 = 0 + 6.166666667

Reorder the terms:
-6.166666667 + 6.166666667 + 2.5x + x2 = 0 + 6.166666667

Combine like terms: -6.166666667 + 6.166666667 = 0.000000000
0.000000000 + 2.5x + x2 = 0 + 6.166666667
2.5x + x2 = 0 + 6.166666667

Combine like terms: 0 + 6.166666667 = 6.166666667
2.5x + x2 = 6.166666667

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 6.166666667 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 6.166666667 + 1.5625

Combine like terms: 6.166666667 + 1.5625 = 7.729166667
1.5625 + 2.5x + x2 = 7.729166667

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 7.729166667

Calculate the square root of the right side: 2.780137886

Break this problem into two subproblems by setting 
(x + 1.25) equal to 2.780137886 and -2.780137886.

Subproblem 1

x + 1.25 = 2.780137886 Simplifying x + 1.25 = 2.780137886 Reorder the terms: 1.25 + x = 2.780137886 Solving 1.25 + x = 2.780137886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 2.780137886 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 2.780137886 + -1.25 x = 2.780137886 + -1.25 Combine like terms: 2.780137886 + -1.25 = 1.530137886 x = 1.530137886 Simplifying x = 1.530137886

Subproblem 2

x + 1.25 = -2.780137886 Simplifying x + 1.25 = -2.780137886 Reorder the terms: 1.25 + x = -2.780137886 Solving 1.25 + x = -2.780137886 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -2.780137886 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -2.780137886 + -1.25 x = -2.780137886 + -1.25 Combine like terms: -2.780137886 + -1.25 = -4.030137886 x = -4.030137886 Simplifying x = -4.030137886

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.530137886, -4.030137886}

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