48=x^2+12x-13

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Solution for 48=x^2+12x-13 equation:


Simplifying
48 = x2 + 12x + -13

Reorder the terms:
48 = -13 + 12x + x2

Solving
48 = -13 + 12x + x2

Solving for variable 'x'.

Combine like terms: 48 + 13 = 61
61 + -12x + -1x2 = -13 + 12x + x2 + 13 + -12x + -1x2

Reorder the terms:
61 + -12x + -1x2 = -13 + 13 + 12x + -12x + x2 + -1x2

Combine like terms: -13 + 13 = 0
61 + -12x + -1x2 = 0 + 12x + -12x + x2 + -1x2
61 + -12x + -1x2 = 12x + -12x + x2 + -1x2

Combine like terms: 12x + -12x = 0
61 + -12x + -1x2 = 0 + x2 + -1x2
61 + -12x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
61 + -12x + -1x2 = 0

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

Divide each side by '-1'.
-61 + 12x + x2 = 0

Move the constant term to the right:

Add '61' to each side of the equation.
-61 + 12x + 61 + x2 = 0 + 61

Reorder the terms:
-61 + 61 + 12x + x2 = 0 + 61

Combine like terms: -61 + 61 = 0
0 + 12x + x2 = 0 + 61
12x + x2 = 0 + 61

Combine like terms: 0 + 61 = 61
12x + x2 = 61

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = 61 + 36

Reorder the terms:
36 + 12x + x2 = 61 + 36

Combine like terms: 61 + 36 = 97
36 + 12x + x2 = 97

Factor a perfect square on the left side:
(x + 6)(x + 6) = 97

Calculate the square root of the right side: 9.848857802

Break this problem into two subproblems by setting 
(x + 6) equal to 9.848857802 and -9.848857802.

Subproblem 1

x + 6 = 9.848857802 Simplifying x + 6 = 9.848857802 Reorder the terms: 6 + x = 9.848857802 Solving 6 + x = 9.848857802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 9.848857802 + -6 Combine like terms: 6 + -6 = 0 0 + x = 9.848857802 + -6 x = 9.848857802 + -6 Combine like terms: 9.848857802 + -6 = 3.848857802 x = 3.848857802 Simplifying x = 3.848857802

Subproblem 2

x + 6 = -9.848857802 Simplifying x + 6 = -9.848857802 Reorder the terms: 6 + x = -9.848857802 Solving 6 + x = -9.848857802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -9.848857802 + -6 Combine like terms: 6 + -6 = 0 0 + x = -9.848857802 + -6 x = -9.848857802 + -6 Combine like terms: -9.848857802 + -6 = -15.848857802 x = -15.848857802 Simplifying x = -15.848857802

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.848857802, -15.848857802}

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