x^2=17x+7

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Solution for x^2=17x+7 equation:


Simplifying
x2 = 17x + 7

Reorder the terms:
x2 = 7 + 17x

Solving
x2 = 7 + 17x

Solving for variable 'x'.

Reorder the terms:
-7 + -17x + x2 = 7 + 17x + -7 + -17x

Reorder the terms:
-7 + -17x + x2 = 7 + -7 + 17x + -17x

Combine like terms: 7 + -7 = 0
-7 + -17x + x2 = 0 + 17x + -17x
-7 + -17x + x2 = 17x + -17x

Combine like terms: 17x + -17x = 0
-7 + -17x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -17x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -17x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -17x + x2 = 0 + 7
-17x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-17x + x2 = 7

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 = 7 + 72.25

Reorder the terms:
72.25 + -17x + x2 = 7 + 72.25

Combine like terms: 7 + 72.25 = 79.25
72.25 + -17x + x2 = 79.25

Factor a perfect square on the left side:
(x + -8.5)(x + -8.5) = 79.25

Calculate the square root of the right side: 8.902246907

Break this problem into two subproblems by setting 
(x + -8.5) equal to 8.902246907 and -8.902246907.

Subproblem 1

x + -8.5 = 8.902246907 Simplifying x + -8.5 = 8.902246907 Reorder the terms: -8.5 + x = 8.902246907 Solving -8.5 + x = 8.902246907 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 = 8.902246907 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 8.902246907 + 8.5 x = 8.902246907 + 8.5 Combine like terms: 8.902246907 + 8.5 = 17.402246907 x = 17.402246907 Simplifying x = 17.402246907

Subproblem 2

x + -8.5 = -8.902246907 Simplifying x + -8.5 = -8.902246907 Reorder the terms: -8.5 + x = -8.902246907 Solving -8.5 + x = -8.902246907 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 = -8.902246907 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -8.902246907 + 8.5 x = -8.902246907 + 8.5 Combine like terms: -8.902246907 + 8.5 = -0.402246907 x = -0.402246907 Simplifying x = -0.402246907

Solution

The solution to the problem is based on the solutions from the subproblems. x = {17.402246907, -0.402246907}

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