4x^2-67x-289=0

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Solution for 4x^2-67x-289=0 equation:


Simplifying
4x2 + -67x + -289 = 0

Reorder the terms:
-289 + -67x + 4x2 = 0

Solving
-289 + -67x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-72.25 + -16.75x + x2 = 0

Move the constant term to the right:

Add '72.25' to each side of the equation.
-72.25 + -16.75x + 72.25 + x2 = 0 + 72.25

Reorder the terms:
-72.25 + 72.25 + -16.75x + x2 = 0 + 72.25

Combine like terms: -72.25 + 72.25 = 0.00
0.00 + -16.75x + x2 = 0 + 72.25
-16.75x + x2 = 0 + 72.25

Combine like terms: 0 + 72.25 = 72.25
-16.75x + x2 = 72.25

The x term is -16.75x.  Take half its coefficient (-8.375).
Square it (70.140625) and add it to both sides.

Add '70.140625' to each side of the equation.
-16.75x + 70.140625 + x2 = 72.25 + 70.140625

Reorder the terms:
70.140625 + -16.75x + x2 = 72.25 + 70.140625

Combine like terms: 72.25 + 70.140625 = 142.390625
70.140625 + -16.75x + x2 = 142.390625

Factor a perfect square on the left side:
(x + -8.375)(x + -8.375) = 142.390625

Calculate the square root of the right side: 11.932754292

Break this problem into two subproblems by setting 
(x + -8.375) equal to 11.932754292 and -11.932754292.

Subproblem 1

x + -8.375 = 11.932754292 Simplifying x + -8.375 = 11.932754292 Reorder the terms: -8.375 + x = 11.932754292 Solving -8.375 + x = 11.932754292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.375' to each side of the equation. -8.375 + 8.375 + x = 11.932754292 + 8.375 Combine like terms: -8.375 + 8.375 = 0.000 0.000 + x = 11.932754292 + 8.375 x = 11.932754292 + 8.375 Combine like terms: 11.932754292 + 8.375 = 20.307754292 x = 20.307754292 Simplifying x = 20.307754292

Subproblem 2

x + -8.375 = -11.932754292 Simplifying x + -8.375 = -11.932754292 Reorder the terms: -8.375 + x = -11.932754292 Solving -8.375 + x = -11.932754292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.375' to each side of the equation. -8.375 + 8.375 + x = -11.932754292 + 8.375 Combine like terms: -8.375 + 8.375 = 0.000 0.000 + x = -11.932754292 + 8.375 x = -11.932754292 + 8.375 Combine like terms: -11.932754292 + 8.375 = -3.557754292 x = -3.557754292 Simplifying x = -3.557754292

Solution

The solution to the problem is based on the solutions from the subproblems. x = {20.307754292, -3.557754292}

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