x^2+34x=144

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Solution for x^2+34x=144 equation:


Simplifying
x2 + 34x = 144

Reorder the terms:
34x + x2 = 144

Solving
34x + x2 = 144

Solving for variable 'x'.

Reorder the terms:
-144 + 34x + x2 = 144 + -144

Combine like terms: 144 + -144 = 0
-144 + 34x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '144' to each side of the equation.
-144 + 34x + 144 + x2 = 0 + 144

Reorder the terms:
-144 + 144 + 34x + x2 = 0 + 144

Combine like terms: -144 + 144 = 0
0 + 34x + x2 = 0 + 144
34x + x2 = 0 + 144

Combine like terms: 0 + 144 = 144
34x + x2 = 144

The x term is 34x.  Take half its coefficient (17).
Square it (289) and add it to both sides.

Add '289' to each side of the equation.
34x + 289 + x2 = 144 + 289

Reorder the terms:
289 + 34x + x2 = 144 + 289

Combine like terms: 144 + 289 = 433
289 + 34x + x2 = 433

Factor a perfect square on the left side:
(x + 17)(x + 17) = 433

Calculate the square root of the right side: 20.808652047

Break this problem into two subproblems by setting 
(x + 17) equal to 20.808652047 and -20.808652047.

Subproblem 1

x + 17 = 20.808652047 Simplifying x + 17 = 20.808652047 Reorder the terms: 17 + x = 20.808652047 Solving 17 + x = 20.808652047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = 20.808652047 + -17 Combine like terms: 17 + -17 = 0 0 + x = 20.808652047 + -17 x = 20.808652047 + -17 Combine like terms: 20.808652047 + -17 = 3.808652047 x = 3.808652047 Simplifying x = 3.808652047

Subproblem 2

x + 17 = -20.808652047 Simplifying x + 17 = -20.808652047 Reorder the terms: 17 + x = -20.808652047 Solving 17 + x = -20.808652047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17' to each side of the equation. 17 + -17 + x = -20.808652047 + -17 Combine like terms: 17 + -17 = 0 0 + x = -20.808652047 + -17 x = -20.808652047 + -17 Combine like terms: -20.808652047 + -17 = -37.808652047 x = -37.808652047 Simplifying x = -37.808652047

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.808652047, -37.808652047}

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