-x^2+4x=-51

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Solution for -x^2+4x=-51 equation:


Simplifying
-1x2 + 4x = -51

Reorder the terms:
4x + -1x2 = -51

Solving
4x + -1x2 = -51

Solving for variable 'x'.

Reorder the terms:
51 + 4x + -1x2 = -51 + 51

Combine like terms: -51 + 51 = 0
51 + 4x + -1x2 = 0

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

Divide each side by '-1'.
-51 + -4x + x2 = 0

Move the constant term to the right:

Add '51' to each side of the equation.
-51 + -4x + 51 + x2 = 0 + 51

Reorder the terms:
-51 + 51 + -4x + x2 = 0 + 51

Combine like terms: -51 + 51 = 0
0 + -4x + x2 = 0 + 51
-4x + x2 = 0 + 51

Combine like terms: 0 + 51 = 51
-4x + x2 = 51

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 51 + 4

Reorder the terms:
4 + -4x + x2 = 51 + 4

Combine like terms: 51 + 4 = 55
4 + -4x + x2 = 55

Factor a perfect square on the left side:
(x + -2)(x + -2) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(x + -2) equal to 7.416198487 and -7.416198487.

Subproblem 1

x + -2 = 7.416198487 Simplifying x + -2 = 7.416198487 Reorder the terms: -2 + x = 7.416198487 Solving -2 + x = 7.416198487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 7.416198487 + 2 Combine like terms: -2 + 2 = 0 0 + x = 7.416198487 + 2 x = 7.416198487 + 2 Combine like terms: 7.416198487 + 2 = 9.416198487 x = 9.416198487 Simplifying x = 9.416198487

Subproblem 2

x + -2 = -7.416198487 Simplifying x + -2 = -7.416198487 Reorder the terms: -2 + x = -7.416198487 Solving -2 + x = -7.416198487 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -7.416198487 + 2 Combine like terms: -2 + 2 = 0 0 + x = -7.416198487 + 2 x = -7.416198487 + 2 Combine like terms: -7.416198487 + 2 = -5.416198487 x = -5.416198487 Simplifying x = -5.416198487

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.416198487, -5.416198487}

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