x^2+62x-200=0

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Solution for x^2+62x-200=0 equation:


Simplifying
x2 + 62x + -200 = 0

Reorder the terms:
-200 + 62x + x2 = 0

Solving
-200 + 62x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '200' to each side of the equation.
-200 + 62x + 200 + x2 = 0 + 200

Reorder the terms:
-200 + 200 + 62x + x2 = 0 + 200

Combine like terms: -200 + 200 = 0
0 + 62x + x2 = 0 + 200
62x + x2 = 0 + 200

Combine like terms: 0 + 200 = 200
62x + x2 = 200

The x term is 62x.  Take half its coefficient (31).
Square it (961) and add it to both sides.

Add '961' to each side of the equation.
62x + 961 + x2 = 200 + 961

Reorder the terms:
961 + 62x + x2 = 200 + 961

Combine like terms: 200 + 961 = 1161
961 + 62x + x2 = 1161

Factor a perfect square on the left side:
(x + 31)(x + 31) = 1161

Calculate the square root of the right side: 34.073450075

Break this problem into two subproblems by setting 
(x + 31) equal to 34.073450075 and -34.073450075.

Subproblem 1

x + 31 = 34.073450075 Simplifying x + 31 = 34.073450075 Reorder the terms: 31 + x = 34.073450075 Solving 31 + x = 34.073450075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + x = 34.073450075 + -31 Combine like terms: 31 + -31 = 0 0 + x = 34.073450075 + -31 x = 34.073450075 + -31 Combine like terms: 34.073450075 + -31 = 3.073450075 x = 3.073450075 Simplifying x = 3.073450075

Subproblem 2

x + 31 = -34.073450075 Simplifying x + 31 = -34.073450075 Reorder the terms: 31 + x = -34.073450075 Solving 31 + x = -34.073450075 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + x = -34.073450075 + -31 Combine like terms: 31 + -31 = 0 0 + x = -34.073450075 + -31 x = -34.073450075 + -31 Combine like terms: -34.073450075 + -31 = -65.073450075 x = -65.073450075 Simplifying x = -65.073450075

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.073450075, -65.073450075}

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