x^2-12x+31=63

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Solution for x^2-12x+31=63 equation:


Simplifying
x2 + -12x + 31 = 63

Reorder the terms:
31 + -12x + x2 = 63

Solving
31 + -12x + x2 = 63

Solving for variable 'x'.

Reorder the terms:
31 + -63 + -12x + x2 = 63 + -63

Combine like terms: 31 + -63 = -32
-32 + -12x + x2 = 63 + -63

Combine like terms: 63 + -63 = 0
-32 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + -12x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + -12x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -12x + x2 = 0 + 32
-12x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
-12x + x2 = 32

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = 32 + 36

Reorder the terms:
36 + -12x + x2 = 32 + 36

Combine like terms: 32 + 36 = 68
36 + -12x + x2 = 68

Factor a perfect square on the left side:
(x + -6)(x + -6) = 68

Calculate the square root of the right side: 8.246211251

Break this problem into two subproblems by setting 
(x + -6) equal to 8.246211251 and -8.246211251.

Subproblem 1

x + -6 = 8.246211251 Simplifying x + -6 = 8.246211251 Reorder the terms: -6 + x = 8.246211251 Solving -6 + x = 8.246211251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 8.246211251 + 6 Combine like terms: -6 + 6 = 0 0 + x = 8.246211251 + 6 x = 8.246211251 + 6 Combine like terms: 8.246211251 + 6 = 14.246211251 x = 14.246211251 Simplifying x = 14.246211251

Subproblem 2

x + -6 = -8.246211251 Simplifying x + -6 = -8.246211251 Reorder the terms: -6 + x = -8.246211251 Solving -6 + x = -8.246211251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -8.246211251 + 6 Combine like terms: -6 + 6 = 0 0 + x = -8.246211251 + 6 x = -8.246211251 + 6 Combine like terms: -8.246211251 + 6 = -2.246211251 x = -2.246211251 Simplifying x = -2.246211251

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.246211251, -2.246211251}

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