5x^2-4x-76=

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Solution for 5x^2-4x-76= equation:


Simplifying
5x2 + -4x + -76 = 0

Reorder the terms:
-76 + -4x + 5x2 = 0

Solving
-76 + -4x + 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'.
-15.2 + -0.8x + x2 = 0

Move the constant term to the right:

Add '15.2' to each side of the equation.
-15.2 + -0.8x + 15.2 + x2 = 0 + 15.2

Reorder the terms:
-15.2 + 15.2 + -0.8x + x2 = 0 + 15.2

Combine like terms: -15.2 + 15.2 = 0.0
0.0 + -0.8x + x2 = 0 + 15.2
-0.8x + x2 = 0 + 15.2

Combine like terms: 0 + 15.2 = 15.2
-0.8x + x2 = 15.2

The x term is -0.8x.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8x + 0.16 + x2 = 15.2 + 0.16

Reorder the terms:
0.16 + -0.8x + x2 = 15.2 + 0.16

Combine like terms: 15.2 + 0.16 = 15.36
0.16 + -0.8x + x2 = 15.36

Factor a perfect square on the left side:
(x + -0.4)(x + -0.4) = 15.36

Calculate the square root of the right side: 3.919183588

Break this problem into two subproblems by setting 
(x + -0.4) equal to 3.919183588 and -3.919183588.

Subproblem 1

x + -0.4 = 3.919183588 Simplifying x + -0.4 = 3.919183588 Reorder the terms: -0.4 + x = 3.919183588 Solving -0.4 + x = 3.919183588 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 3.919183588 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 3.919183588 + 0.4 x = 3.919183588 + 0.4 Combine like terms: 3.919183588 + 0.4 = 4.319183588 x = 4.319183588 Simplifying x = 4.319183588

Subproblem 2

x + -0.4 = -3.919183588 Simplifying x + -0.4 = -3.919183588 Reorder the terms: -0.4 + x = -3.919183588 Solving -0.4 + x = -3.919183588 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -3.919183588 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -3.919183588 + 0.4 x = -3.919183588 + 0.4 Combine like terms: -3.919183588 + 0.4 = -3.519183588 x = -3.519183588 Simplifying x = -3.519183588

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.319183588, -3.519183588}

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