225=8x+x^2

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Solution for 225=8x+x^2 equation:


Simplifying
225 = 8x + x2

Solving
225 = 8x + x2

Solving for variable 'x'.

Reorder the terms:
225 + -8x + -1x2 = 8x + -8x + x2 + -1x2

Combine like terms: 8x + -8x = 0
225 + -8x + -1x2 = 0 + x2 + -1x2
225 + -8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
225 + -8x + -1x2 = 0

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

Divide each side by '-1'.
-225 + 8x + x2 = 0

Move the constant term to the right:

Add '225' to each side of the equation.
-225 + 8x + 225 + x2 = 0 + 225

Reorder the terms:
-225 + 225 + 8x + x2 = 0 + 225

Combine like terms: -225 + 225 = 0
0 + 8x + x2 = 0 + 225
8x + x2 = 0 + 225

Combine like terms: 0 + 225 = 225
8x + x2 = 225

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 225 + 16

Reorder the terms:
16 + 8x + x2 = 225 + 16

Combine like terms: 225 + 16 = 241
16 + 8x + x2 = 241

Factor a perfect square on the left side:
(x + 4)(x + 4) = 241

Calculate the square root of the right side: 15.524174696

Break this problem into two subproblems by setting 
(x + 4) equal to 15.524174696 and -15.524174696.

Subproblem 1

x + 4 = 15.524174696 Simplifying x + 4 = 15.524174696 Reorder the terms: 4 + x = 15.524174696 Solving 4 + x = 15.524174696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 15.524174696 + -4 Combine like terms: 4 + -4 = 0 0 + x = 15.524174696 + -4 x = 15.524174696 + -4 Combine like terms: 15.524174696 + -4 = 11.524174696 x = 11.524174696 Simplifying x = 11.524174696

Subproblem 2

x + 4 = -15.524174696 Simplifying x + 4 = -15.524174696 Reorder the terms: 4 + x = -15.524174696 Solving 4 + x = -15.524174696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -15.524174696 + -4 Combine like terms: 4 + -4 = 0 0 + x = -15.524174696 + -4 x = -15.524174696 + -4 Combine like terms: -15.524174696 + -4 = -19.524174696 x = -19.524174696 Simplifying x = -19.524174696

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.524174696, -19.524174696}

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