-50+5x+x^2=48

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Solution for -50+5x+x^2=48 equation:


Simplifying
-50 + 5x + x2 = 48

Solving
-50 + 5x + x2 = 48

Solving for variable 'x'.

Reorder the terms:
-50 + -48 + 5x + x2 = 48 + -48

Combine like terms: -50 + -48 = -98
-98 + 5x + x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-98 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '98' to each side of the equation.
-98 + 5x + 98 + x2 = 0 + 98

Reorder the terms:
-98 + 98 + 5x + x2 = 0 + 98

Combine like terms: -98 + 98 = 0
0 + 5x + x2 = 0 + 98
5x + x2 = 0 + 98

Combine like terms: 0 + 98 = 98
5x + x2 = 98

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 98 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 98 + 6.25

Combine like terms: 98 + 6.25 = 104.25
6.25 + 5x + x2 = 104.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 104.25

Calculate the square root of the right side: 10.210288928

Break this problem into two subproblems by setting 
(x + 2.5) equal to 10.210288928 and -10.210288928.

Subproblem 1

x + 2.5 = 10.210288928 Simplifying x + 2.5 = 10.210288928 Reorder the terms: 2.5 + x = 10.210288928 Solving 2.5 + x = 10.210288928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 10.210288928 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 10.210288928 + -2.5 x = 10.210288928 + -2.5 Combine like terms: 10.210288928 + -2.5 = 7.710288928 x = 7.710288928 Simplifying x = 7.710288928

Subproblem 2

x + 2.5 = -10.210288928 Simplifying x + 2.5 = -10.210288928 Reorder the terms: 2.5 + x = -10.210288928 Solving 2.5 + x = -10.210288928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -10.210288928 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -10.210288928 + -2.5 x = -10.210288928 + -2.5 Combine like terms: -10.210288928 + -2.5 = -12.710288928 x = -12.710288928 Simplifying x = -12.710288928

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.710288928, -12.710288928}

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