8x^2+19x-37=0

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Solution for 8x^2+19x-37=0 equation:


Simplifying
8x2 + 19x + -37 = 0

Reorder the terms:
-37 + 19x + 8x2 = 0

Solving
-37 + 19x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
-4.625 + 2.375x + x2 = 0

Move the constant term to the right:

Add '4.625' to each side of the equation.
-4.625 + 2.375x + 4.625 + x2 = 0 + 4.625

Reorder the terms:
-4.625 + 4.625 + 2.375x + x2 = 0 + 4.625

Combine like terms: -4.625 + 4.625 = 0.000
0.000 + 2.375x + x2 = 0 + 4.625
2.375x + x2 = 0 + 4.625

Combine like terms: 0 + 4.625 = 4.625
2.375x + x2 = 4.625

The x term is 2.375x.  Take half its coefficient (1.1875).
Square it (1.41015625) and add it to both sides.

Add '1.41015625' to each side of the equation.
2.375x + 1.41015625 + x2 = 4.625 + 1.41015625

Reorder the terms:
1.41015625 + 2.375x + x2 = 4.625 + 1.41015625

Combine like terms: 4.625 + 1.41015625 = 6.03515625
1.41015625 + 2.375x + x2 = 6.03515625

Factor a perfect square on the left side:
(x + 1.1875)(x + 1.1875) = 6.03515625

Calculate the square root of the right side: 2.456655501

Break this problem into two subproblems by setting 
(x + 1.1875) equal to 2.456655501 and -2.456655501.

Subproblem 1

x + 1.1875 = 2.456655501 Simplifying x + 1.1875 = 2.456655501 Reorder the terms: 1.1875 + x = 2.456655501 Solving 1.1875 + x = 2.456655501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1875' to each side of the equation. 1.1875 + -1.1875 + x = 2.456655501 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + x = 2.456655501 + -1.1875 x = 2.456655501 + -1.1875 Combine like terms: 2.456655501 + -1.1875 = 1.269155501 x = 1.269155501 Simplifying x = 1.269155501

Subproblem 2

x + 1.1875 = -2.456655501 Simplifying x + 1.1875 = -2.456655501 Reorder the terms: 1.1875 + x = -2.456655501 Solving 1.1875 + x = -2.456655501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.1875' to each side of the equation. 1.1875 + -1.1875 + x = -2.456655501 + -1.1875 Combine like terms: 1.1875 + -1.1875 = 0.0000 0.0000 + x = -2.456655501 + -1.1875 x = -2.456655501 + -1.1875 Combine like terms: -2.456655501 + -1.1875 = -3.644155501 x = -3.644155501 Simplifying x = -3.644155501

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.269155501, -3.644155501}

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