x^2+3x=34

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Solution for x^2+3x=34 equation:


Simplifying
x2 + 3x = 34

Reorder the terms:
3x + x2 = 34

Solving
3x + x2 = 34

Solving for variable 'x'.

Reorder the terms:
-34 + 3x + x2 = 34 + -34

Combine like terms: 34 + -34 = 0
-34 + 3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '34' to each side of the equation.
-34 + 3x + 34 + x2 = 0 + 34

Reorder the terms:
-34 + 34 + 3x + x2 = 0 + 34

Combine like terms: -34 + 34 = 0
0 + 3x + x2 = 0 + 34
3x + x2 = 0 + 34

Combine like terms: 0 + 34 = 34
3x + x2 = 34

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 = 34 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 34 + 2.25

Combine like terms: 34 + 2.25 = 36.25
2.25 + 3x + x2 = 36.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 36.25

Calculate the square root of the right side: 6.020797289

Break this problem into two subproblems by setting 
(x + 1.5) equal to 6.020797289 and -6.020797289.

Subproblem 1

x + 1.5 = 6.020797289 Simplifying x + 1.5 = 6.020797289 Reorder the terms: 1.5 + x = 6.020797289 Solving 1.5 + x = 6.020797289 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 = 6.020797289 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 6.020797289 + -1.5 x = 6.020797289 + -1.5 Combine like terms: 6.020797289 + -1.5 = 4.520797289 x = 4.520797289 Simplifying x = 4.520797289

Subproblem 2

x + 1.5 = -6.020797289 Simplifying x + 1.5 = -6.020797289 Reorder the terms: 1.5 + x = -6.020797289 Solving 1.5 + x = -6.020797289 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 = -6.020797289 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -6.020797289 + -1.5 x = -6.020797289 + -1.5 Combine like terms: -6.020797289 + -1.5 = -7.520797289 x = -7.520797289 Simplifying x = -7.520797289

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.520797289, -7.520797289}

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