0=X^2-3.5X-3.0625

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Solution for 0=X^2-3.5X-3.0625 equation:


Simplifying
0 = X2 + -3.5X + -3.0625

Reorder the terms:
0 = -3.0625 + -3.5X + X2

Solving
0 = -3.0625 + -3.5X + X2

Solving for variable 'X'.

Combine like terms: 0 + 3.0625 = 3.0625
3.0625 + 3.5X + -1X2 = -3.0625 + -3.5X + X2 + 3.0625 + 3.5X + -1X2

Reorder the terms:
3.0625 + 3.5X + -1X2 = -3.0625 + 3.0625 + -3.5X + 3.5X + X2 + -1X2

Combine like terms: -3.0625 + 3.0625 = 0.0000
3.0625 + 3.5X + -1X2 = 0.0000 + -3.5X + 3.5X + X2 + -1X2
3.0625 + 3.5X + -1X2 = -3.5X + 3.5X + X2 + -1X2

Combine like terms: -3.5X + 3.5X = 0.0
3.0625 + 3.5X + -1X2 = 0.0 + X2 + -1X2
3.0625 + 3.5X + -1X2 = X2 + -1X2

Combine like terms: X2 + -1X2 = 0
3.0625 + 3.5X + -1X2 = 0

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

Divide each side by '-1'.
-3.0625 + -3.5X + X2 = 0

Move the constant term to the right:

Add '3.0625' to each side of the equation.
-3.0625 + -3.5X + 3.0625 + X2 = 0 + 3.0625

Reorder the terms:
-3.0625 + 3.0625 + -3.5X + X2 = 0 + 3.0625

Combine like terms: -3.0625 + 3.0625 = 0.0000
0.0000 + -3.5X + X2 = 0 + 3.0625
-3.5X + X2 = 0 + 3.0625

Combine like terms: 0 + 3.0625 = 3.0625
-3.5X + X2 = 3.0625

The X term is -3.5X.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5X + 3.0625 + X2 = 3.0625 + 3.0625

Reorder the terms:
3.0625 + -3.5X + X2 = 3.0625 + 3.0625

Combine like terms: 3.0625 + 3.0625 = 6.125
3.0625 + -3.5X + X2 = 6.125

Factor a perfect square on the left side:
(X + -1.75)(X + -1.75) = 6.125

Calculate the square root of the right side: 2.474873734

Break this problem into two subproblems by setting 
(X + -1.75) equal to 2.474873734 and -2.474873734.

Subproblem 1

X + -1.75 = 2.474873734 Simplifying X + -1.75 = 2.474873734 Reorder the terms: -1.75 + X = 2.474873734 Solving -1.75 + X = 2.474873734 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + X = 2.474873734 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + X = 2.474873734 + 1.75 X = 2.474873734 + 1.75 Combine like terms: 2.474873734 + 1.75 = 4.224873734 X = 4.224873734 Simplifying X = 4.224873734

Subproblem 2

X + -1.75 = -2.474873734 Simplifying X + -1.75 = -2.474873734 Reorder the terms: -1.75 + X = -2.474873734 Solving -1.75 + X = -2.474873734 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + X = -2.474873734 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + X = -2.474873734 + 1.75 X = -2.474873734 + 1.75 Combine like terms: -2.474873734 + 1.75 = -0.724873734 X = -0.724873734 Simplifying X = -0.724873734

Solution

The solution to the problem is based on the solutions from the subproblems. X = {4.224873734, -0.724873734}

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