x^2+30x=122

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Solution for x^2+30x=122 equation:


Simplifying
x2 + 30x = 122

Reorder the terms:
30x + x2 = 122

Solving
30x + x2 = 122

Solving for variable 'x'.

Reorder the terms:
-122 + 30x + x2 = 122 + -122

Combine like terms: 122 + -122 = 0
-122 + 30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '122' to each side of the equation.
-122 + 30x + 122 + x2 = 0 + 122

Reorder the terms:
-122 + 122 + 30x + x2 = 0 + 122

Combine like terms: -122 + 122 = 0
0 + 30x + x2 = 0 + 122
30x + x2 = 0 + 122

Combine like terms: 0 + 122 = 122
30x + x2 = 122

The x term is 30x.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30x + 225 + x2 = 122 + 225

Reorder the terms:
225 + 30x + x2 = 122 + 225

Combine like terms: 122 + 225 = 347
225 + 30x + x2 = 347

Factor a perfect square on the left side:
(x + 15)(x + 15) = 347

Calculate the square root of the right side: 18.62793601

Break this problem into two subproblems by setting 
(x + 15) equal to 18.62793601 and -18.62793601.

Subproblem 1

x + 15 = 18.62793601 Simplifying x + 15 = 18.62793601 Reorder the terms: 15 + x = 18.62793601 Solving 15 + x = 18.62793601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 18.62793601 + -15 Combine like terms: 15 + -15 = 0 0 + x = 18.62793601 + -15 x = 18.62793601 + -15 Combine like terms: 18.62793601 + -15 = 3.62793601 x = 3.62793601 Simplifying x = 3.62793601

Subproblem 2

x + 15 = -18.62793601 Simplifying x + 15 = -18.62793601 Reorder the terms: 15 + x = -18.62793601 Solving 15 + x = -18.62793601 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -18.62793601 + -15 Combine like terms: 15 + -15 = 0 0 + x = -18.62793601 + -15 x = -18.62793601 + -15 Combine like terms: -18.62793601 + -15 = -33.62793601 x = -33.62793601 Simplifying x = -33.62793601

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.62793601, -33.62793601}

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