x^2+2x-11.25=0

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Solution for x^2+2x-11.25=0 equation:


Simplifying
x2 + 2x + -11.25 = 0

Reorder the terms:
-11.25 + 2x + x2 = 0

Solving
-11.25 + 2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '11.25' to each side of the equation.
-11.25 + 2x + 11.25 + x2 = 0 + 11.25

Reorder the terms:
-11.25 + 11.25 + 2x + x2 = 0 + 11.25

Combine like terms: -11.25 + 11.25 = 0.00
0.00 + 2x + x2 = 0 + 11.25
2x + x2 = 0 + 11.25

Combine like terms: 0 + 11.25 = 11.25
2x + x2 = 11.25

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 11.25 + 1

Reorder the terms:
1 + 2x + x2 = 11.25 + 1

Combine like terms: 11.25 + 1 = 12.25
1 + 2x + x2 = 12.25

Factor a perfect square on the left side:
(x + 1)(x + 1) = 12.25

Calculate the square root of the right side: 3.5

Break this problem into two subproblems by setting 
(x + 1) equal to 3.5 and -3.5.

Subproblem 1

x + 1 = 3.5 Simplifying x + 1 = 3.5 Reorder the terms: 1 + x = 3.5 Solving 1 + x = 3.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.5 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.5 + -1 x = 3.5 + -1 Combine like terms: 3.5 + -1 = 2.5 x = 2.5 Simplifying x = 2.5

Subproblem 2

x + 1 = -3.5 Simplifying x + 1 = -3.5 Reorder the terms: 1 + x = -3.5 Solving 1 + x = -3.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.5 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.5 + -1 x = -3.5 + -1 Combine like terms: -3.5 + -1 = -4.5 x = -4.5 Simplifying x = -4.5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.5, -4.5}

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