x^2-14x-51=3

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Solution for x^2-14x-51=3 equation:


Simplifying
x2 + -14x + -51 = 3

Reorder the terms:
-51 + -14x + x2 = 3

Solving
-51 + -14x + x2 = 3

Solving for variable 'x'.

Reorder the terms:
-51 + -3 + -14x + x2 = 3 + -3

Combine like terms: -51 + -3 = -54
-54 + -14x + x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-54 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '54' to each side of the equation.
-54 + -14x + 54 + x2 = 0 + 54

Reorder the terms:
-54 + 54 + -14x + x2 = 0 + 54

Combine like terms: -54 + 54 = 0
0 + -14x + x2 = 0 + 54
-14x + x2 = 0 + 54

Combine like terms: 0 + 54 = 54
-14x + x2 = 54

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = 54 + 49

Reorder the terms:
49 + -14x + x2 = 54 + 49

Combine like terms: 54 + 49 = 103
49 + -14x + x2 = 103

Factor a perfect square on the left side:
(x + -7)(x + -7) = 103

Calculate the square root of the right side: 10.148891565

Break this problem into two subproblems by setting 
(x + -7) equal to 10.148891565 and -10.148891565.

Subproblem 1

x + -7 = 10.148891565 Simplifying x + -7 = 10.148891565 Reorder the terms: -7 + x = 10.148891565 Solving -7 + x = 10.148891565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 10.148891565 + 7 Combine like terms: -7 + 7 = 0 0 + x = 10.148891565 + 7 x = 10.148891565 + 7 Combine like terms: 10.148891565 + 7 = 17.148891565 x = 17.148891565 Simplifying x = 17.148891565

Subproblem 2

x + -7 = -10.148891565 Simplifying x + -7 = -10.148891565 Reorder the terms: -7 + x = -10.148891565 Solving -7 + x = -10.148891565 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -10.148891565 + 7 Combine like terms: -7 + 7 = 0 0 + x = -10.148891565 + 7 x = -10.148891565 + 7 Combine like terms: -10.148891565 + 7 = -3.148891565 x = -3.148891565 Simplifying x = -3.148891565

Solution

The solution to the problem is based on the solutions from the subproblems. x = {17.148891565, -3.148891565}

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