4x^2-19x-51=0

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Solution for 4x^2-19x-51=0 equation:


Simplifying
4x2 + -19x + -51 = 0

Reorder the terms:
-51 + -19x + 4x2 = 0

Solving
-51 + -19x + 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'.
-12.75 + -4.75x + x2 = 0

Move the constant term to the right:

Add '12.75' to each side of the equation.
-12.75 + -4.75x + 12.75 + x2 = 0 + 12.75

Reorder the terms:
-12.75 + 12.75 + -4.75x + x2 = 0 + 12.75

Combine like terms: -12.75 + 12.75 = 0.00
0.00 + -4.75x + x2 = 0 + 12.75
-4.75x + x2 = 0 + 12.75

Combine like terms: 0 + 12.75 = 12.75
-4.75x + x2 = 12.75

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 = 12.75 + 5.640625

Reorder the terms:
5.640625 + -4.75x + x2 = 12.75 + 5.640625

Combine like terms: 12.75 + 5.640625 = 18.390625
5.640625 + -4.75x + x2 = 18.390625

Factor a perfect square on the left side:
(x + -2.375)(x + -2.375) = 18.390625

Calculate the square root of the right side: 4.2884292

Break this problem into two subproblems by setting 
(x + -2.375) equal to 4.2884292 and -4.2884292.

Subproblem 1

x + -2.375 = 4.2884292 Simplifying x + -2.375 = 4.2884292 Reorder the terms: -2.375 + x = 4.2884292 Solving -2.375 + x = 4.2884292 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 = 4.2884292 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = 4.2884292 + 2.375 x = 4.2884292 + 2.375 Combine like terms: 4.2884292 + 2.375 = 6.6634292 x = 6.6634292 Simplifying x = 6.6634292

Subproblem 2

x + -2.375 = -4.2884292 Simplifying x + -2.375 = -4.2884292 Reorder the terms: -2.375 + x = -4.2884292 Solving -2.375 + x = -4.2884292 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 = -4.2884292 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + x = -4.2884292 + 2.375 x = -4.2884292 + 2.375 Combine like terms: -4.2884292 + 2.375 = -1.9134292 x = -1.9134292 Simplifying x = -1.9134292

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.6634292, -1.9134292}

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