x^2-3x-17=49

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Solution for x^2-3x-17=49 equation:


Simplifying
x2 + -3x + -17 = 49

Reorder the terms:
-17 + -3x + x2 = 49

Solving
-17 + -3x + x2 = 49

Solving for variable 'x'.

Reorder the terms:
-17 + -49 + -3x + x2 = 49 + -49

Combine like terms: -17 + -49 = -66
-66 + -3x + x2 = 49 + -49

Combine like terms: 49 + -49 = 0
-66 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '66' to each side of the equation.
-66 + -3x + 66 + x2 = 0 + 66

Reorder the terms:
-66 + 66 + -3x + x2 = 0 + 66

Combine like terms: -66 + 66 = 0
0 + -3x + x2 = 0 + 66
-3x + x2 = 0 + 66

Combine like terms: 0 + 66 = 66
-3x + x2 = 66

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 66 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 66 + 2.25

Combine like terms: 66 + 2.25 = 68.25
2.25 + -3x + x2 = 68.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 68.25

Calculate the square root of the right side: 8.261355821

Break this problem into two subproblems by setting 
(x + -1.5) equal to 8.261355821 and -8.261355821.

Subproblem 1

x + -1.5 = 8.261355821 Simplifying x + -1.5 = 8.261355821 Reorder the terms: -1.5 + x = 8.261355821 Solving -1.5 + x = 8.261355821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 8.261355821 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 8.261355821 + 1.5 x = 8.261355821 + 1.5 Combine like terms: 8.261355821 + 1.5 = 9.761355821 x = 9.761355821 Simplifying x = 9.761355821

Subproblem 2

x + -1.5 = -8.261355821 Simplifying x + -1.5 = -8.261355821 Reorder the terms: -1.5 + x = -8.261355821 Solving -1.5 + x = -8.261355821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -8.261355821 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -8.261355821 + 1.5 x = -8.261355821 + 1.5 Combine like terms: -8.261355821 + 1.5 = -6.761355821 x = -6.761355821 Simplifying x = -6.761355821

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.761355821, -6.761355821}

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