4x^2-89x-360=0

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Solution for 4x^2-89x-360=0 equation:


Simplifying
4x2 + -89x + -360 = 0

Reorder the terms:
-360 + -89x + 4x2 = 0

Solving
-360 + -89x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-90 + -22.25x + x2 = 0

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + -22.25x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + -22.25x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + -22.25x + x2 = 0 + 90
-22.25x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
-22.25x + x2 = 90

The x term is -22.25x.  Take half its coefficient (-11.125).
Square it (123.765625) and add it to both sides.

Add '123.765625' to each side of the equation.
-22.25x + 123.765625 + x2 = 90 + 123.765625

Reorder the terms:
123.765625 + -22.25x + x2 = 90 + 123.765625

Combine like terms: 90 + 123.765625 = 213.765625
123.765625 + -22.25x + x2 = 213.765625

Factor a perfect square on the left side:
(x + -11.125)(x + -11.125) = 213.765625

Calculate the square root of the right side: 14.620725871

Break this problem into two subproblems by setting 
(x + -11.125) equal to 14.620725871 and -14.620725871.

Subproblem 1

x + -11.125 = 14.620725871 Simplifying x + -11.125 = 14.620725871 Reorder the terms: -11.125 + x = 14.620725871 Solving -11.125 + x = 14.620725871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.125' to each side of the equation. -11.125 + 11.125 + x = 14.620725871 + 11.125 Combine like terms: -11.125 + 11.125 = 0.000 0.000 + x = 14.620725871 + 11.125 x = 14.620725871 + 11.125 Combine like terms: 14.620725871 + 11.125 = 25.745725871 x = 25.745725871 Simplifying x = 25.745725871

Subproblem 2

x + -11.125 = -14.620725871 Simplifying x + -11.125 = -14.620725871 Reorder the terms: -11.125 + x = -14.620725871 Solving -11.125 + x = -14.620725871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.125' to each side of the equation. -11.125 + 11.125 + x = -14.620725871 + 11.125 Combine like terms: -11.125 + 11.125 = 0.000 0.000 + x = -14.620725871 + 11.125 x = -14.620725871 + 11.125 Combine like terms: -14.620725871 + 11.125 = -3.495725871 x = -3.495725871 Simplifying x = -3.495725871

Solution

The solution to the problem is based on the solutions from the subproblems. x = {25.745725871, -3.495725871}

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