x^2+40x+17=

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Solution for x^2+40x+17= equation:


Simplifying
x2 + 40x + 17 = 0

Reorder the terms:
17 + 40x + x2 = 0

Solving
17 + 40x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + 40x + -17 + x2 = 0 + -17

Reorder the terms:
17 + -17 + 40x + x2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + 40x + x2 = 0 + -17
40x + x2 = 0 + -17

Combine like terms: 0 + -17 = -17
40x + x2 = -17

The x term is 40x.  Take half its coefficient (20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
40x + 400 + x2 = -17 + 400

Reorder the terms:
400 + 40x + x2 = -17 + 400

Combine like terms: -17 + 400 = 383
400 + 40x + x2 = 383

Factor a perfect square on the left side:
(x + 20)(x + 20) = 383

Calculate the square root of the right side: 19.570385791

Break this problem into two subproblems by setting 
(x + 20) equal to 19.570385791 and -19.570385791.

Subproblem 1

x + 20 = 19.570385791 Simplifying x + 20 = 19.570385791 Reorder the terms: 20 + x = 19.570385791 Solving 20 + x = 19.570385791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 19.570385791 + -20 Combine like terms: 20 + -20 = 0 0 + x = 19.570385791 + -20 x = 19.570385791 + -20 Combine like terms: 19.570385791 + -20 = -0.429614209 x = -0.429614209 Simplifying x = -0.429614209

Subproblem 2

x + 20 = -19.570385791 Simplifying x + 20 = -19.570385791 Reorder the terms: 20 + x = -19.570385791 Solving 20 + x = -19.570385791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -19.570385791 + -20 Combine like terms: 20 + -20 = 0 0 + x = -19.570385791 + -20 x = -19.570385791 + -20 Combine like terms: -19.570385791 + -20 = -39.570385791 x = -39.570385791 Simplifying x = -39.570385791

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.429614209, -39.570385791}

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