-x^2+4x+53=0

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Solution for -x^2+4x+53=0 equation:


Simplifying
-1x2 + 4x + 53 = 0

Reorder the terms:
53 + 4x + -1x2 = 0

Solving
53 + 4x + -1x2 = 0

Solving for variable 'x'.

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

Divide each side by '-1'.
-53 + -4x + x2 = 0

Move the constant term to the right:

Add '53' to each side of the equation.
-53 + -4x + 53 + x2 = 0 + 53

Reorder the terms:
-53 + 53 + -4x + x2 = 0 + 53

Combine like terms: -53 + 53 = 0
0 + -4x + x2 = 0 + 53
-4x + x2 = 0 + 53

Combine like terms: 0 + 53 = 53
-4x + x2 = 53

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 = 53 + 4

Reorder the terms:
4 + -4x + x2 = 53 + 4

Combine like terms: 53 + 4 = 57
4 + -4x + x2 = 57

Factor a perfect square on the left side:
(x + -2)(x + -2) = 57

Calculate the square root of the right side: 7.549834435

Break this problem into two subproblems by setting 
(x + -2) equal to 7.549834435 and -7.549834435.

Subproblem 1

x + -2 = 7.549834435 Simplifying x + -2 = 7.549834435 Reorder the terms: -2 + x = 7.549834435 Solving -2 + x = 7.549834435 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 = 7.549834435 + 2 Combine like terms: -2 + 2 = 0 0 + x = 7.549834435 + 2 x = 7.549834435 + 2 Combine like terms: 7.549834435 + 2 = 9.549834435 x = 9.549834435 Simplifying x = 9.549834435

Subproblem 2

x + -2 = -7.549834435 Simplifying x + -2 = -7.549834435 Reorder the terms: -2 + x = -7.549834435 Solving -2 + x = -7.549834435 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 = -7.549834435 + 2 Combine like terms: -2 + 2 = 0 0 + x = -7.549834435 + 2 x = -7.549834435 + 2 Combine like terms: -7.549834435 + 2 = -5.549834435 x = -5.549834435 Simplifying x = -5.549834435

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.549834435, -5.549834435}

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