x^2=50x+7

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Solution for x^2=50x+7 equation:


Simplifying
x2 = 50x + 7

Reorder the terms:
x2 = 7 + 50x

Solving
x2 = 7 + 50x

Solving for variable 'x'.

Reorder the terms:
-7 + -50x + x2 = 7 + 50x + -7 + -50x

Reorder the terms:
-7 + -50x + x2 = 7 + -7 + 50x + -50x

Combine like terms: 7 + -7 = 0
-7 + -50x + x2 = 0 + 50x + -50x
-7 + -50x + x2 = 50x + -50x

Combine like terms: 50x + -50x = 0
-7 + -50x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -50x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -50x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -50x + x2 = 0 + 7
-50x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-50x + x2 = 7

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 = 7 + 625

Reorder the terms:
625 + -50x + x2 = 7 + 625

Combine like terms: 7 + 625 = 632
625 + -50x + x2 = 632

Factor a perfect square on the left side:
(x + -25)(x + -25) = 632

Calculate the square root of the right side: 25.13961018

Break this problem into two subproblems by setting 
(x + -25) equal to 25.13961018 and -25.13961018.

Subproblem 1

x + -25 = 25.13961018 Simplifying x + -25 = 25.13961018 Reorder the terms: -25 + x = 25.13961018 Solving -25 + x = 25.13961018 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 = 25.13961018 + 25 Combine like terms: -25 + 25 = 0 0 + x = 25.13961018 + 25 x = 25.13961018 + 25 Combine like terms: 25.13961018 + 25 = 50.13961018 x = 50.13961018 Simplifying x = 50.13961018

Subproblem 2

x + -25 = -25.13961018 Simplifying x + -25 = -25.13961018 Reorder the terms: -25 + x = -25.13961018 Solving -25 + x = -25.13961018 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 = -25.13961018 + 25 Combine like terms: -25 + 25 = 0 0 + x = -25.13961018 + 25 x = -25.13961018 + 25 Combine like terms: -25.13961018 + 25 = -0.13961018 x = -0.13961018 Simplifying x = -0.13961018

Solution

The solution to the problem is based on the solutions from the subproblems. x = {50.13961018, -0.13961018}

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