x^2+2.5x-9=0

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Solution for x^2+2.5x-9=0 equation:


Simplifying
x2 + 2.5x + -9 = 0

Reorder the terms:
-9 + 2.5x + x2 = 0

Solving
-9 + 2.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 2.5x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + 2.5x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 2.5x + x2 = 0 + 9
2.5x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
2.5x + x2 = 9

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 = 9 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 9 + 1.5625

Combine like terms: 9 + 1.5625 = 10.5625
1.5625 + 2.5x + x2 = 10.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 10.5625

Calculate the square root of the right side: 3.25

Break this problem into two subproblems by setting 
(x + 1.25) equal to 3.25 and -3.25.

Subproblem 1

x + 1.25 = 3.25 Simplifying x + 1.25 = 3.25 Reorder the terms: 1.25 + x = 3.25 Solving 1.25 + x = 3.25 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 = 3.25 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 3.25 + -1.25 x = 3.25 + -1.25 Combine like terms: 3.25 + -1.25 = 2 x = 2 Simplifying x = 2

Subproblem 2

x + 1.25 = -3.25 Simplifying x + 1.25 = -3.25 Reorder the terms: 1.25 + x = -3.25 Solving 1.25 + x = -3.25 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 = -3.25 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -3.25 + -1.25 x = -3.25 + -1.25 Combine like terms: -3.25 + -1.25 = -4.5 x = -4.5 Simplifying x = -4.5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2, -4.5}

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