x(7+5)=2x^2-17x+48

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Solution for x(7+5)=2x^2-17x+48 equation:


Simplifying
x(7 + 5) = 2x2 + -17x + 48

Combine like terms: 7 + 5 = 12
x(12) = 2x2 + -17x + 48

Reorder the terms for easier multiplication:
12x = 2x2 + -17x + 48

Reorder the terms:
12x = 48 + -17x + 2x2

Solving
12x = 48 + -17x + 2x2

Solving for variable 'x'.

Reorder the terms:
-48 + 12x + 17x + -2x2 = 48 + -17x + 2x2 + -48 + 17x + -2x2

Combine like terms: 12x + 17x = 29x
-48 + 29x + -2x2 = 48 + -17x + 2x2 + -48 + 17x + -2x2

Reorder the terms:
-48 + 29x + -2x2 = 48 + -48 + -17x + 17x + 2x2 + -2x2

Combine like terms: 48 + -48 = 0
-48 + 29x + -2x2 = 0 + -17x + 17x + 2x2 + -2x2
-48 + 29x + -2x2 = -17x + 17x + 2x2 + -2x2

Combine like terms: -17x + 17x = 0
-48 + 29x + -2x2 = 0 + 2x2 + -2x2
-48 + 29x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-48 + 29x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
24 + -14.5x + x2 = 0

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + -14.5x + -24 + x2 = 0 + -24

Reorder the terms:
24 + -24 + -14.5x + x2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -14.5x + x2 = 0 + -24
-14.5x + x2 = 0 + -24

Combine like terms: 0 + -24 = -24
-14.5x + x2 = -24

The x term is -14.5x.  Take half its coefficient (-7.25).
Square it (52.5625) and add it to both sides.

Add '52.5625' to each side of the equation.
-14.5x + 52.5625 + x2 = -24 + 52.5625

Reorder the terms:
52.5625 + -14.5x + x2 = -24 + 52.5625

Combine like terms: -24 + 52.5625 = 28.5625
52.5625 + -14.5x + x2 = 28.5625

Factor a perfect square on the left side:
(x + -7.25)(x + -7.25) = 28.5625

Calculate the square root of the right side: 5.344389582

Break this problem into two subproblems by setting 
(x + -7.25) equal to 5.344389582 and -5.344389582.

Subproblem 1

x + -7.25 = 5.344389582 Simplifying x + -7.25 = 5.344389582 Reorder the terms: -7.25 + x = 5.344389582 Solving -7.25 + x = 5.344389582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.25' to each side of the equation. -7.25 + 7.25 + x = 5.344389582 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + x = 5.344389582 + 7.25 x = 5.344389582 + 7.25 Combine like terms: 5.344389582 + 7.25 = 12.594389582 x = 12.594389582 Simplifying x = 12.594389582

Subproblem 2

x + -7.25 = -5.344389582 Simplifying x + -7.25 = -5.344389582 Reorder the terms: -7.25 + x = -5.344389582 Solving -7.25 + x = -5.344389582 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.25' to each side of the equation. -7.25 + 7.25 + x = -5.344389582 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + x = -5.344389582 + 7.25 x = -5.344389582 + 7.25 Combine like terms: -5.344389582 + 7.25 = 1.905610418 x = 1.905610418 Simplifying x = 1.905610418

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.594389582, 1.905610418}

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