37x^2-21x=178

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Solution for 37x^2-21x=178 equation:


Simplifying
37x2 + -21x = 178

Reorder the terms:
-21x + 37x2 = 178

Solving
-21x + 37x2 = 178

Solving for variable 'x'.

Reorder the terms:
-178 + -21x + 37x2 = 178 + -178

Combine like terms: 178 + -178 = 0
-178 + -21x + 37x2 = 0

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

Divide each side by '37'.
-4.810810811 + -0.5675675676x + x2 = 0

Move the constant term to the right:

Add '4.810810811' to each side of the equation.
-4.810810811 + -0.5675675676x + 4.810810811 + x2 = 0 + 4.810810811

Reorder the terms:
-4.810810811 + 4.810810811 + -0.5675675676x + x2 = 0 + 4.810810811

Combine like terms: -4.810810811 + 4.810810811 = 0.000000000
0.000000000 + -0.5675675676x + x2 = 0 + 4.810810811
-0.5675675676x + x2 = 0 + 4.810810811

Combine like terms: 0 + 4.810810811 = 4.810810811
-0.5675675676x + x2 = 4.810810811

The x term is -0.5675675676x.  Take half its coefficient (-0.2837837838).
Square it (0.08053323595) and add it to both sides.

Add '0.08053323595' to each side of the equation.
-0.5675675676x + 0.08053323595 + x2 = 4.810810811 + 0.08053323595

Reorder the terms:
0.08053323595 + -0.5675675676x + x2 = 4.810810811 + 0.08053323595

Combine like terms: 4.810810811 + 0.08053323595 = 4.89134404695
0.08053323595 + -0.5675675676x + x2 = 4.89134404695

Factor a perfect square on the left side:
(x + -0.2837837838)(x + -0.2837837838) = 4.89134404695

Calculate the square root of the right side: 2.211638317

Break this problem into two subproblems by setting 
(x + -0.2837837838) equal to 2.211638317 and -2.211638317.

Subproblem 1

x + -0.2837837838 = 2.211638317 Simplifying x + -0.2837837838 = 2.211638317 Reorder the terms: -0.2837837838 + x = 2.211638317 Solving -0.2837837838 + x = 2.211638317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2837837838' to each side of the equation. -0.2837837838 + 0.2837837838 + x = 2.211638317 + 0.2837837838 Combine like terms: -0.2837837838 + 0.2837837838 = 0.0000000000 0.0000000000 + x = 2.211638317 + 0.2837837838 x = 2.211638317 + 0.2837837838 Combine like terms: 2.211638317 + 0.2837837838 = 2.4954221008 x = 2.4954221008 Simplifying x = 2.4954221008

Subproblem 2

x + -0.2837837838 = -2.211638317 Simplifying x + -0.2837837838 = -2.211638317 Reorder the terms: -0.2837837838 + x = -2.211638317 Solving -0.2837837838 + x = -2.211638317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2837837838' to each side of the equation. -0.2837837838 + 0.2837837838 + x = -2.211638317 + 0.2837837838 Combine like terms: -0.2837837838 + 0.2837837838 = 0.0000000000 0.0000000000 + x = -2.211638317 + 0.2837837838 x = -2.211638317 + 0.2837837838 Combine like terms: -2.211638317 + 0.2837837838 = -1.9278545332 x = -1.9278545332 Simplifying x = -1.9278545332

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.4954221008, -1.9278545332}

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