x^2-10x+3=7

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Solution for x^2-10x+3=7 equation:


Simplifying
x2 + -10x + 3 = 7

Reorder the terms:
3 + -10x + x2 = 7

Solving
3 + -10x + x2 = 7

Solving for variable 'x'.

Reorder the terms:
3 + -7 + -10x + x2 = 7 + -7

Combine like terms: 3 + -7 = -4
-4 + -10x + x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-4 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -10x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -10x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -10x + x2 = 0 + 4
-10x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-10x + x2 = 4

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 = 4 + 25

Reorder the terms:
25 + -10x + x2 = 4 + 25

Combine like terms: 4 + 25 = 29
25 + -10x + x2 = 29

Factor a perfect square on the left side:
(x + -5)(x + -5) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(x + -5) equal to 5.385164807 and -5.385164807.

Subproblem 1

x + -5 = 5.385164807 Simplifying x + -5 = 5.385164807 Reorder the terms: -5 + x = 5.385164807 Solving -5 + x = 5.385164807 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 = 5.385164807 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.385164807 + 5 x = 5.385164807 + 5 Combine like terms: 5.385164807 + 5 = 10.385164807 x = 10.385164807 Simplifying x = 10.385164807

Subproblem 2

x + -5 = -5.385164807 Simplifying x + -5 = -5.385164807 Reorder the terms: -5 + x = -5.385164807 Solving -5 + x = -5.385164807 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 = -5.385164807 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.385164807 + 5 x = -5.385164807 + 5 Combine like terms: -5.385164807 + 5 = -0.385164807 x = -0.385164807 Simplifying x = -0.385164807

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.385164807, -0.385164807}

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