0=x^2+2x-30

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Solution for 0=x^2+2x-30 equation:


Simplifying
0 = x2 + 2x + -30

Reorder the terms:
0 = -30 + 2x + x2

Solving
0 = -30 + 2x + x2

Solving for variable 'x'.

Combine like terms: 0 + 30 = 30
30 + -2x + -1x2 = -30 + 2x + x2 + 30 + -2x + -1x2

Reorder the terms:
30 + -2x + -1x2 = -30 + 30 + 2x + -2x + x2 + -1x2

Combine like terms: -30 + 30 = 0
30 + -2x + -1x2 = 0 + 2x + -2x + x2 + -1x2
30 + -2x + -1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
30 + -2x + -1x2 = 0 + x2 + -1x2
30 + -2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
30 + -2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-30 + 2x + x2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 2x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 2x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 2x + x2 = 0 + 30
2x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
2x + x2 = 30

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 = 30 + 1

Reorder the terms:
1 + 2x + x2 = 30 + 1

Combine like terms: 30 + 1 = 31
1 + 2x + x2 = 31

Factor a perfect square on the left side:
(x + 1)(x + 1) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(x + 1) equal to 5.567764363 and -5.567764363.

Subproblem 1

x + 1 = 5.567764363 Simplifying x + 1 = 5.567764363 Reorder the terms: 1 + x = 5.567764363 Solving 1 + x = 5.567764363 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 = 5.567764363 + -1 Combine like terms: 1 + -1 = 0 0 + x = 5.567764363 + -1 x = 5.567764363 + -1 Combine like terms: 5.567764363 + -1 = 4.567764363 x = 4.567764363 Simplifying x = 4.567764363

Subproblem 2

x + 1 = -5.567764363 Simplifying x + 1 = -5.567764363 Reorder the terms: 1 + x = -5.567764363 Solving 1 + x = -5.567764363 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 = -5.567764363 + -1 Combine like terms: 1 + -1 = 0 0 + x = -5.567764363 + -1 x = -5.567764363 + -1 Combine like terms: -5.567764363 + -1 = -6.567764363 x = -6.567764363 Simplifying x = -6.567764363

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.567764363, -6.567764363}

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