x^2-10x=3

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Solution for x^2-10x=3 equation:


Simplifying
x2 + -10x = 3

Reorder the terms:
-10x + x2 = 3

Solving
-10x + x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + -10x + x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -10x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -10x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -10x + x2 = 0 + 3
-10x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-10x + x2 = 3

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 3 + 25

Reorder the terms:
25 + -10x + x2 = 3 + 25

Combine like terms: 3 + 25 = 28
25 + -10x + x2 = 28

Factor a perfect square on the left side:
(x + -5)(x + -5) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(x + -5) equal to 5.291502622 and -5.291502622.

Subproblem 1

x + -5 = 5.291502622 Simplifying x + -5 = 5.291502622 Reorder the terms: -5 + x = 5.291502622 Solving -5 + x = 5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 5.291502622 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.291502622 + 5 x = 5.291502622 + 5 Combine like terms: 5.291502622 + 5 = 10.291502622 x = 10.291502622 Simplifying x = 10.291502622

Subproblem 2

x + -5 = -5.291502622 Simplifying x + -5 = -5.291502622 Reorder the terms: -5 + x = -5.291502622 Solving -5 + x = -5.291502622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -5.291502622 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.291502622 + 5 x = -5.291502622 + 5 Combine like terms: -5.291502622 + 5 = -0.291502622 x = -0.291502622 Simplifying x = -0.291502622

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.291502622, -0.291502622}

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