3x^2+6x-175=0

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Solution for 3x^2+6x-175=0 equation:


Simplifying
3x2 + 6x + -175 = 0

Reorder the terms:
-175 + 6x + 3x2 = 0

Solving
-175 + 6x + 3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-58.33333333 + 2x + x2 = 0

Move the constant term to the right:

Add '58.33333333' to each side of the equation.
-58.33333333 + 2x + 58.33333333 + x2 = 0 + 58.33333333

Reorder the terms:
-58.33333333 + 58.33333333 + 2x + x2 = 0 + 58.33333333

Combine like terms: -58.33333333 + 58.33333333 = 0.00000000
0.00000000 + 2x + x2 = 0 + 58.33333333
2x + x2 = 0 + 58.33333333

Combine like terms: 0 + 58.33333333 = 58.33333333
2x + x2 = 58.33333333

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 58.33333333 + 1

Reorder the terms:
1 + 2x + x2 = 58.33333333 + 1

Combine like terms: 58.33333333 + 1 = 59.33333333
1 + 2x + x2 = 59.33333333

Factor a perfect square on the left side:
(x + 1)(x + 1) = 59.33333333

Calculate the square root of the right side: 7.702813339

Break this problem into two subproblems by setting 
(x + 1) equal to 7.702813339 and -7.702813339.

Subproblem 1

x + 1 = 7.702813339 Simplifying x + 1 = 7.702813339 Reorder the terms: 1 + x = 7.702813339 Solving 1 + x = 7.702813339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 7.702813339 + -1 Combine like terms: 1 + -1 = 0 0 + x = 7.702813339 + -1 x = 7.702813339 + -1 Combine like terms: 7.702813339 + -1 = 6.702813339 x = 6.702813339 Simplifying x = 6.702813339

Subproblem 2

x + 1 = -7.702813339 Simplifying x + 1 = -7.702813339 Reorder the terms: 1 + x = -7.702813339 Solving 1 + x = -7.702813339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -7.702813339 + -1 Combine like terms: 1 + -1 = 0 0 + x = -7.702813339 + -1 x = -7.702813339 + -1 Combine like terms: -7.702813339 + -1 = -8.702813339 x = -8.702813339 Simplifying x = -8.702813339

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.702813339, -8.702813339}

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