1-2x(x+50)=0

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Solution for 1-2x(x+50)=0 equation:


Simplifying
1 + -2x(x + 50) = 0

Reorder the terms:
1 + -2x(50 + x) = 0
1 + (50 * -2x + x * -2x) = 0
1 + (-100x + -2x2) = 0

Solving
1 + -100x + -2x2 = 0

Solving for variable 'x'.

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

Divide each side by '-2'.
-0.5 + 50x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 50x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 50x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 50x + x2 = 0 + 0.5
50x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
50x + x2 = 0.5

The x term is 50x.  Take half its coefficient (25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
50x + 625 + x2 = 0.5 + 625

Reorder the terms:
625 + 50x + x2 = 0.5 + 625

Combine like terms: 0.5 + 625 = 625.5
625 + 50x + x2 = 625.5

Factor a perfect square on the left side:
(x + 25)(x + 25) = 625.5

Calculate the square root of the right side: 25.009998001

Break this problem into two subproblems by setting 
(x + 25) equal to 25.009998001 and -25.009998001.

Subproblem 1

x + 25 = 25.009998001 Simplifying x + 25 = 25.009998001 Reorder the terms: 25 + x = 25.009998001 Solving 25 + x = 25.009998001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 25.009998001 + -25 Combine like terms: 25 + -25 = 0 0 + x = 25.009998001 + -25 x = 25.009998001 + -25 Combine like terms: 25.009998001 + -25 = 0.009998001 x = 0.009998001 Simplifying x = 0.009998001

Subproblem 2

x + 25 = -25.009998001 Simplifying x + 25 = -25.009998001 Reorder the terms: 25 + x = -25.009998001 Solving 25 + x = -25.009998001 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = -25.009998001 + -25 Combine like terms: 25 + -25 = 0 0 + x = -25.009998001 + -25 x = -25.009998001 + -25 Combine like terms: -25.009998001 + -25 = -50.009998001 x = -50.009998001 Simplifying x = -50.009998001

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.009998001, -50.009998001}

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