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Simplifying
x2 + 3x + -10 = 0

Reorder the terms:
-10 + 3x + x2 = 0

Solving
-10 + 3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 3x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 3x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 3x + x2 = 0 + 10
3x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
3x + x2 = 10

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 10 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 10 + 2.25

Combine like terms: 10 + 2.25 = 12.25
2.25 + 3x + x2 = 12.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 12.25

Calculate the square root of the right side: 3.5

Break this problem into two subproblems by setting 
(x + 1.5) equal to 3.5 and -3.5.

Subproblem 1

x + 1.5 = 3.5 Simplifying x + 1.5 = 3.5 Reorder the terms: 1.5 + x = 3.5 Solving 1.5 + x = 3.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 3.5 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 3.5 + -1.5 x = 3.5 + -1.5 Combine like terms: 3.5 + -1.5 = 2 x = 2 Simplifying x = 2

Subproblem 2

x + 1.5 = -3.5 Simplifying x + 1.5 = -3.5 Reorder the terms: 1.5 + x = -3.5 Solving 1.5 + x = -3.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -3.5 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -3.5 + -1.5 x = -3.5 + -1.5 Combine like terms: -3.5 + -1.5 = -5 x = -5 Simplifying x = -5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2, -5}
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