356x+x^2=100

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Solution for 356x+x^2=100 equation:


Simplifying
356x + x2 = 100

Solving
356x + x2 = 100

Solving for variable 'x'.

Reorder the terms:
-100 + 356x + x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + 356x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '100' to each side of the equation.
-100 + 356x + 100 + x2 = 0 + 100

Reorder the terms:
-100 + 100 + 356x + x2 = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 356x + x2 = 0 + 100
356x + x2 = 0 + 100

Combine like terms: 0 + 100 = 100
356x + x2 = 100

The x term is 356x.  Take half its coefficient (178).
Square it (31684) and add it to both sides.

Add '31684' to each side of the equation.
356x + 31684 + x2 = 100 + 31684

Reorder the terms:
31684 + 356x + x2 = 100 + 31684

Combine like terms: 100 + 31684 = 31784
31684 + 356x + x2 = 31784

Factor a perfect square on the left side:
(x + 178)(x + 178) = 31784

Calculate the square root of the right side: 178.280677585

Break this problem into two subproblems by setting 
(x + 178) equal to 178.280677585 and -178.280677585.

Subproblem 1

x + 178 = 178.280677585 Simplifying x + 178 = 178.280677585 Reorder the terms: 178 + x = 178.280677585 Solving 178 + x = 178.280677585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-178' to each side of the equation. 178 + -178 + x = 178.280677585 + -178 Combine like terms: 178 + -178 = 0 0 + x = 178.280677585 + -178 x = 178.280677585 + -178 Combine like terms: 178.280677585 + -178 = 0.280677585 x = 0.280677585 Simplifying x = 0.280677585

Subproblem 2

x + 178 = -178.280677585 Simplifying x + 178 = -178.280677585 Reorder the terms: 178 + x = -178.280677585 Solving 178 + x = -178.280677585 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-178' to each side of the equation. 178 + -178 + x = -178.280677585 + -178 Combine like terms: 178 + -178 = 0 0 + x = -178.280677585 + -178 x = -178.280677585 + -178 Combine like terms: -178.280677585 + -178 = -356.280677585 x = -356.280677585 Simplifying x = -356.280677585

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.280677585, -356.280677585}

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