x^2+3x+2=100

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Solution for x^2+3x+2=100 equation:


Simplifying
x2 + 3x + 2 = 100

Reorder the terms:
2 + 3x + x2 = 100

Solving
2 + 3x + x2 = 100

Solving for variable 'x'.

Reorder the terms:
2 + -100 + 3x + x2 = 100 + -100

Combine like terms: 2 + -100 = -98
-98 + 3x + x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-98 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '98' to each side of the equation.
-98 + 3x + 98 + x2 = 0 + 98

Reorder the terms:
-98 + 98 + 3x + x2 = 0 + 98

Combine like terms: -98 + 98 = 0
0 + 3x + x2 = 0 + 98
3x + x2 = 0 + 98

Combine like terms: 0 + 98 = 98
3x + x2 = 98

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 = 98 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 98 + 2.25

Combine like terms: 98 + 2.25 = 100.25
2.25 + 3x + x2 = 100.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 100.25

Calculate the square root of the right side: 10.012492197

Break this problem into two subproblems by setting 
(x + 1.5) equal to 10.012492197 and -10.012492197.

Subproblem 1

x + 1.5 = 10.012492197 Simplifying x + 1.5 = 10.012492197 Reorder the terms: 1.5 + x = 10.012492197 Solving 1.5 + x = 10.012492197 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 = 10.012492197 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 10.012492197 + -1.5 x = 10.012492197 + -1.5 Combine like terms: 10.012492197 + -1.5 = 8.512492197 x = 8.512492197 Simplifying x = 8.512492197

Subproblem 2

x + 1.5 = -10.012492197 Simplifying x + 1.5 = -10.012492197 Reorder the terms: 1.5 + x = -10.012492197 Solving 1.5 + x = -10.012492197 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 = -10.012492197 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -10.012492197 + -1.5 x = -10.012492197 + -1.5 Combine like terms: -10.012492197 + -1.5 = -11.512492197 x = -11.512492197 Simplifying x = -11.512492197

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.512492197, -11.512492197}

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