x^2-3x-100=9

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Solution for x^2-3x-100=9 equation:


Simplifying
x2 + -3x + -100 = 9

Reorder the terms:
-100 + -3x + x2 = 9

Solving
-100 + -3x + x2 = 9

Solving for variable 'x'.

Reorder the terms:
-100 + -9 + -3x + x2 = 9 + -9

Combine like terms: -100 + -9 = -109
-109 + -3x + x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-109 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '109' to each side of the equation.
-109 + -3x + 109 + x2 = 0 + 109

Reorder the terms:
-109 + 109 + -3x + x2 = 0 + 109

Combine like terms: -109 + 109 = 0
0 + -3x + x2 = 0 + 109
-3x + x2 = 0 + 109

Combine like terms: 0 + 109 = 109
-3x + x2 = 109

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 = 109 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 109 + 2.25

Combine like terms: 109 + 2.25 = 111.25
2.25 + -3x + x2 = 111.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 111.25

Calculate the square root of the right side: 10.547511555

Break this problem into two subproblems by setting 
(x + -1.5) equal to 10.547511555 and -10.547511555.

Subproblem 1

x + -1.5 = 10.547511555 Simplifying x + -1.5 = 10.547511555 Reorder the terms: -1.5 + x = 10.547511555 Solving -1.5 + x = 10.547511555 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 = 10.547511555 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 10.547511555 + 1.5 x = 10.547511555 + 1.5 Combine like terms: 10.547511555 + 1.5 = 12.047511555 x = 12.047511555 Simplifying x = 12.047511555

Subproblem 2

x + -1.5 = -10.547511555 Simplifying x + -1.5 = -10.547511555 Reorder the terms: -1.5 + x = -10.547511555 Solving -1.5 + x = -10.547511555 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 = -10.547511555 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -10.547511555 + 1.5 x = -10.547511555 + 1.5 Combine like terms: -10.547511555 + 1.5 = -9.047511555 x = -9.047511555 Simplifying x = -9.047511555

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.047511555, -9.047511555}

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