x^2-2.5x-75=0

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Solution for x^2-2.5x-75=0 equation:


Simplifying
x2 + -2.5x + -75 = 0

Reorder the terms:
-75 + -2.5x + x2 = 0

Solving
-75 + -2.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '75' to each side of the equation.
-75 + -2.5x + 75 + x2 = 0 + 75

Reorder the terms:
-75 + 75 + -2.5x + x2 = 0 + 75

Combine like terms: -75 + 75 = 0
0 + -2.5x + x2 = 0 + 75
-2.5x + x2 = 0 + 75

Combine like terms: 0 + 75 = 75
-2.5x + x2 = 75

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 75 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 75 + 1.5625

Combine like terms: 75 + 1.5625 = 76.5625
1.5625 + -2.5x + x2 = 76.5625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 76.5625

Calculate the square root of the right side: 8.75

Break this problem into two subproblems by setting 
(x + -1.25) equal to 8.75 and -8.75.

Subproblem 1

x + -1.25 = 8.75 Simplifying x + -1.25 = 8.75 Reorder the terms: -1.25 + x = 8.75 Solving -1.25 + x = 8.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 8.75 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 8.75 + 1.25 x = 8.75 + 1.25 Combine like terms: 8.75 + 1.25 = 10 x = 10 Simplifying x = 10

Subproblem 2

x + -1.25 = -8.75 Simplifying x + -1.25 = -8.75 Reorder the terms: -1.25 + x = -8.75 Solving -1.25 + x = -8.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -8.75 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -8.75 + 1.25 x = -8.75 + 1.25 Combine like terms: -8.75 + 1.25 = -7.5 x = -7.5 Simplifying x = -7.5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10, -7.5}

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