2x^2+29.5x-73=0

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Solution for 2x^2+29.5x-73=0 equation:


Simplifying
2x2 + 29.5x + -73 = 0

Reorder the terms:
-73 + 29.5x + 2x2 = 0

Solving
-73 + 29.5x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-36.5 + 14.75x + x2 = 0

Move the constant term to the right:

Add '36.5' to each side of the equation.
-36.5 + 14.75x + 36.5 + x2 = 0 + 36.5

Reorder the terms:
-36.5 + 36.5 + 14.75x + x2 = 0 + 36.5

Combine like terms: -36.5 + 36.5 = 0.0
0.0 + 14.75x + x2 = 0 + 36.5
14.75x + x2 = 0 + 36.5

Combine like terms: 0 + 36.5 = 36.5
14.75x + x2 = 36.5

The x term is 14.75x.  Take half its coefficient (7.375).
Square it (54.390625) and add it to both sides.

Add '54.390625' to each side of the equation.
14.75x + 54.390625 + x2 = 36.5 + 54.390625

Reorder the terms:
54.390625 + 14.75x + x2 = 36.5 + 54.390625

Combine like terms: 36.5 + 54.390625 = 90.890625
54.390625 + 14.75x + x2 = 90.890625

Factor a perfect square on the left side:
(x + 7.375)(x + 7.375) = 90.890625

Calculate the square root of the right side: 9.533657483

Break this problem into two subproblems by setting 
(x + 7.375) equal to 9.533657483 and -9.533657483.

Subproblem 1

x + 7.375 = 9.533657483 Simplifying x + 7.375 = 9.533657483 Reorder the terms: 7.375 + x = 9.533657483 Solving 7.375 + x = 9.533657483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.375' to each side of the equation. 7.375 + -7.375 + x = 9.533657483 + -7.375 Combine like terms: 7.375 + -7.375 = 0.000 0.000 + x = 9.533657483 + -7.375 x = 9.533657483 + -7.375 Combine like terms: 9.533657483 + -7.375 = 2.158657483 x = 2.158657483 Simplifying x = 2.158657483

Subproblem 2

x + 7.375 = -9.533657483 Simplifying x + 7.375 = -9.533657483 Reorder the terms: 7.375 + x = -9.533657483 Solving 7.375 + x = -9.533657483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.375' to each side of the equation. 7.375 + -7.375 + x = -9.533657483 + -7.375 Combine like terms: 7.375 + -7.375 = 0.000 0.000 + x = -9.533657483 + -7.375 x = -9.533657483 + -7.375 Combine like terms: -9.533657483 + -7.375 = -16.908657483 x = -16.908657483 Simplifying x = -16.908657483

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.158657483, -16.908657483}

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