x^2-9.5x-93=0

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Solution for x^2-9.5x-93=0 equation:


Simplifying
x2 + -9.5x + -93 = 0

Reorder the terms:
-93 + -9.5x + x2 = 0

Solving
-93 + -9.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '93' to each side of the equation.
-93 + -9.5x + 93 + x2 = 0 + 93

Reorder the terms:
-93 + 93 + -9.5x + x2 = 0 + 93

Combine like terms: -93 + 93 = 0
0 + -9.5x + x2 = 0 + 93
-9.5x + x2 = 0 + 93

Combine like terms: 0 + 93 = 93
-9.5x + x2 = 93

The x term is -9.5x.  Take half its coefficient (-4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
-9.5x + 22.5625 + x2 = 93 + 22.5625

Reorder the terms:
22.5625 + -9.5x + x2 = 93 + 22.5625

Combine like terms: 93 + 22.5625 = 115.5625
22.5625 + -9.5x + x2 = 115.5625

Factor a perfect square on the left side:
(x + -4.75)(x + -4.75) = 115.5625

Calculate the square root of the right side: 10.75

Break this problem into two subproblems by setting 
(x + -4.75) equal to 10.75 and -10.75.

Subproblem 1

x + -4.75 = 10.75 Simplifying x + -4.75 = 10.75 Reorder the terms: -4.75 + x = 10.75 Solving -4.75 + x = 10.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = 10.75 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = 10.75 + 4.75 x = 10.75 + 4.75 Combine like terms: 10.75 + 4.75 = 15.5 x = 15.5 Simplifying x = 15.5

Subproblem 2

x + -4.75 = -10.75 Simplifying x + -4.75 = -10.75 Reorder the terms: -4.75 + x = -10.75 Solving -4.75 + x = -10.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.75' to each side of the equation. -4.75 + 4.75 + x = -10.75 + 4.75 Combine like terms: -4.75 + 4.75 = 0.00 0.00 + x = -10.75 + 4.75 x = -10.75 + 4.75 Combine like terms: -10.75 + 4.75 = -6 x = -6 Simplifying x = -6

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.5, -6}

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