5x^2-3x-37=0

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Solution for 5x^2-3x-37=0 equation:


Simplifying
5x2 + -3x + -37 = 0

Reorder the terms:
-37 + -3x + 5x2 = 0

Solving
-37 + -3x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-7.4 + -0.6x + x2 = 0

Move the constant term to the right:

Add '7.4' to each side of the equation.
-7.4 + -0.6x + 7.4 + x2 = 0 + 7.4

Reorder the terms:
-7.4 + 7.4 + -0.6x + x2 = 0 + 7.4

Combine like terms: -7.4 + 7.4 = 0.0
0.0 + -0.6x + x2 = 0 + 7.4
-0.6x + x2 = 0 + 7.4

Combine like terms: 0 + 7.4 = 7.4
-0.6x + x2 = 7.4

The x term is -0.6x.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6x + 0.09 + x2 = 7.4 + 0.09

Reorder the terms:
0.09 + -0.6x + x2 = 7.4 + 0.09

Combine like terms: 7.4 + 0.09 = 7.49
0.09 + -0.6x + x2 = 7.49

Factor a perfect square on the left side:
(x + -0.3)(x + -0.3) = 7.49

Calculate the square root of the right side: 2.736786437

Break this problem into two subproblems by setting 
(x + -0.3) equal to 2.736786437 and -2.736786437.

Subproblem 1

x + -0.3 = 2.736786437 Simplifying x + -0.3 = 2.736786437 Reorder the terms: -0.3 + x = 2.736786437 Solving -0.3 + x = 2.736786437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 2.736786437 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 2.736786437 + 0.3 x = 2.736786437 + 0.3 Combine like terms: 2.736786437 + 0.3 = 3.036786437 x = 3.036786437 Simplifying x = 3.036786437

Subproblem 2

x + -0.3 = -2.736786437 Simplifying x + -0.3 = -2.736786437 Reorder the terms: -0.3 + x = -2.736786437 Solving -0.3 + x = -2.736786437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -2.736786437 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -2.736786437 + 0.3 x = -2.736786437 + 0.3 Combine like terms: -2.736786437 + 0.3 = -2.436786437 x = -2.436786437 Simplifying x = -2.436786437

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.036786437, -2.436786437}

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