-x^2+10x=3

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


Simplifying
-1x2 + 10x = 3

Reorder the terms:
10x + -1x2 = 3

Solving
10x + -1x2 = 3

Solving for variable 'x'.

Reorder the terms:
-3 + 10x + -1x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 10x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
3 + -10x + x2 = 0

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 = 22
25 + -10x + x2 = 22

Factor a perfect square on the left side:
(x + -5)(x + -5) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(x + -5) equal to 4.69041576 and -4.69041576.

Subproblem 1

x + -5 = 4.69041576 Simplifying x + -5 = 4.69041576 Reorder the terms: -5 + x = 4.69041576 Solving -5 + x = 4.69041576 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 = 4.69041576 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.69041576 + 5 x = 4.69041576 + 5 Combine like terms: 4.69041576 + 5 = 9.69041576 x = 9.69041576 Simplifying x = 9.69041576

Subproblem 2

x + -5 = -4.69041576 Simplifying x + -5 = -4.69041576 Reorder the terms: -5 + x = -4.69041576 Solving -5 + x = -4.69041576 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 = -4.69041576 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.69041576 + 5 x = -4.69041576 + 5 Combine like terms: -4.69041576 + 5 = 0.30958424 x = 0.30958424 Simplifying x = 0.30958424

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.69041576, 0.30958424}

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