x^2+19x+150=180

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Solution for x^2+19x+150=180 equation:


Simplifying
x2 + 19x + 150 = 180

Reorder the terms:
150 + 19x + x2 = 180

Solving
150 + 19x + x2 = 180

Solving for variable 'x'.

Reorder the terms:
150 + -180 + 19x + x2 = 180 + -180

Combine like terms: 150 + -180 = -30
-30 + 19x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-30 + 19x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 19x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 19x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 19x + x2 = 0 + 30
19x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
19x + x2 = 30

The x term is 19x.  Take half its coefficient (9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
19x + 90.25 + x2 = 30 + 90.25

Reorder the terms:
90.25 + 19x + x2 = 30 + 90.25

Combine like terms: 30 + 90.25 = 120.25
90.25 + 19x + x2 = 120.25

Factor a perfect square on the left side:
(x + 9.5)(x + 9.5) = 120.25

Calculate the square root of the right side: 10.9658561

Break this problem into two subproblems by setting 
(x + 9.5) equal to 10.9658561 and -10.9658561.

Subproblem 1

x + 9.5 = 10.9658561 Simplifying x + 9.5 = 10.9658561 Reorder the terms: 9.5 + x = 10.9658561 Solving 9.5 + x = 10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 10.9658561 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 10.9658561 + -9.5 x = 10.9658561 + -9.5 Combine like terms: 10.9658561 + -9.5 = 1.4658561 x = 1.4658561 Simplifying x = 1.4658561

Subproblem 2

x + 9.5 = -10.9658561 Simplifying x + 9.5 = -10.9658561 Reorder the terms: 9.5 + x = -10.9658561 Solving 9.5 + x = -10.9658561 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -10.9658561 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -10.9658561 + -9.5 x = -10.9658561 + -9.5 Combine like terms: -10.9658561 + -9.5 = -20.4658561 x = -20.4658561 Simplifying x = -20.4658561

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.4658561, -20.4658561}

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