x^2+17x=90

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Solution for x^2+17x=90 equation:


Simplifying
x2 + 17x = 90

Reorder the terms:
17x + x2 = 90

Solving
17x + x2 = 90

Solving for variable 'x'.

Reorder the terms:
-90 + 17x + x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + 17x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 17x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + 17x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 17x + x2 = 0 + 90
17x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
17x + x2 = 90

The x term is 17x.  Take half its coefficient (8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
17x + 72.25 + x2 = 90 + 72.25

Reorder the terms:
72.25 + 17x + x2 = 90 + 72.25

Combine like terms: 90 + 72.25 = 162.25
72.25 + 17x + x2 = 162.25

Factor a perfect square on the left side:
(x + 8.5)(x + 8.5) = 162.25

Calculate the square root of the right side: 12.737739203

Break this problem into two subproblems by setting 
(x + 8.5) equal to 12.737739203 and -12.737739203.

Subproblem 1

x + 8.5 = 12.737739203 Simplifying x + 8.5 = 12.737739203 Reorder the terms: 8.5 + x = 12.737739203 Solving 8.5 + x = 12.737739203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 12.737739203 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 12.737739203 + -8.5 x = 12.737739203 + -8.5 Combine like terms: 12.737739203 + -8.5 = 4.237739203 x = 4.237739203 Simplifying x = 4.237739203

Subproblem 2

x + 8.5 = -12.737739203 Simplifying x + 8.5 = -12.737739203 Reorder the terms: 8.5 + x = -12.737739203 Solving 8.5 + x = -12.737739203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -12.737739203 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -12.737739203 + -8.5 x = -12.737739203 + -8.5 Combine like terms: -12.737739203 + -8.5 = -21.237739203 x = -21.237739203 Simplifying x = -21.237739203

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.237739203, -21.237739203}

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