x^2-4.75x-5.25=0

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Solution for x^2-4.75x-5.25=0 equation:


Simplifying
x2 + -4.75x + -5.25 = 0

Reorder the terms:
-5.25 + -4.75x + x2 = 0

Solving
-5.25 + -4.75x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '5.25' to each side of the equation.
-5.25 + -4.75x + 5.25 + x2 = 0 + 5.25

Reorder the terms:
-5.25 + 5.25 + -4.75x + x2 = 0 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + -4.75x + x2 = 0 + 5.25
-4.75x + x2 = 0 + 5.25

Combine like terms: 0 + 5.25 = 5.25
-4.75x + x2 = 5.25

The x term is -4.75x.  Take half its coefficient (-2.375).
Square it (5.640625) and add it to both sides.

Add '5.640625' to each side of the equation.
-4.75x + 5.640625 + x2 = 5.25 + 5.640625

Reorder the terms:
5.640625 + -4.75x + x2 = 5.25 + 5.640625

Combine like terms: 5.25 + 5.640625 = 10.890625
5.640625 + -4.75x + x2 = 10.890625

Factor a perfect square on the left side:
(x + -2.375)(x + -2.375) = 10.890625

Calculate the square root of the right side: 3.300094696

Break this problem into two subproblems by setting 
(x + -2.375) equal to 3.300094696 and -3.300094696.

Subproblem 1

x + -2.375 = 3.300094696 Simplifying x + -2.375 = 3.300094696 Reorder the terms: -2.375 + x = 3.300094696 Solving -2.375 + x = 3.300094696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = 3.300094696 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = 3.300094696 + 2.375 x = 3.300094696 + 2.375 Combine like terms: 3.300094696 + 2.375 = 5.675094696 x = 5.675094696 Simplifying x = 5.675094696

Subproblem 2

x + -2.375 = -3.300094696 Simplifying x + -2.375 = -3.300094696 Reorder the terms: -2.375 + x = -3.300094696 Solving -2.375 + x = -3.300094696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.375' to each side of the equation. -2.375 + 2.375 + x = -3.300094696 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = -3.300094696 + 2.375 x = -3.300094696 + 2.375 Combine like terms: -3.300094696 + 2.375 = -0.925094696 x = -0.925094696 Simplifying x = -0.925094696

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.675094696, -0.925094696}

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