x+(x-7)(x-7)=17

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Solution for x+(x-7)(x-7)=17 equation:


Simplifying
x + (x + -7)(x + -7) = 17

Reorder the terms:
x + (-7 + x)(x + -7) = 17

Reorder the terms:
x + (-7 + x)(-7 + x) = 17

Multiply (-7 + x) * (-7 + x)
x + (-7(-7 + x) + x(-7 + x)) = 17
x + ((-7 * -7 + x * -7) + x(-7 + x)) = 17
x + ((49 + -7x) + x(-7 + x)) = 17
x + (49 + -7x + (-7 * x + x * x)) = 17
x + (49 + -7x + (-7x + x2)) = 17

Combine like terms: -7x + -7x = -14x
x + (49 + -14x + x2) = 17

Reorder the terms:
49 + x + -14x + x2 = 17

Combine like terms: x + -14x = -13x
49 + -13x + x2 = 17

Solving
49 + -13x + x2 = 17

Solving for variable 'x'.

Reorder the terms:
49 + -17 + -13x + x2 = 17 + -17

Combine like terms: 49 + -17 = 32
32 + -13x + x2 = 17 + -17

Combine like terms: 17 + -17 = 0
32 + -13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-32' to each side of the equation.
32 + -13x + -32 + x2 = 0 + -32

Reorder the terms:
32 + -32 + -13x + x2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + -13x + x2 = 0 + -32
-13x + x2 = 0 + -32

Combine like terms: 0 + -32 = -32
-13x + x2 = -32

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = -32 + 42.25

Reorder the terms:
42.25 + -13x + x2 = -32 + 42.25

Combine like terms: -32 + 42.25 = 10.25
42.25 + -13x + x2 = 10.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(x + -6.5) equal to 3.201562119 and -3.201562119.

Subproblem 1

x + -6.5 = 3.201562119 Simplifying x + -6.5 = 3.201562119 Reorder the terms: -6.5 + x = 3.201562119 Solving -6.5 + x = 3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 3.201562119 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 3.201562119 + 6.5 x = 3.201562119 + 6.5 Combine like terms: 3.201562119 + 6.5 = 9.701562119 x = 9.701562119 Simplifying x = 9.701562119

Subproblem 2

x + -6.5 = -3.201562119 Simplifying x + -6.5 = -3.201562119 Reorder the terms: -6.5 + x = -3.201562119 Solving -6.5 + x = -3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -3.201562119 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -3.201562119 + 6.5 x = -3.201562119 + 6.5 Combine like terms: -3.201562119 + 6.5 = 3.298437881 x = 3.298437881 Simplifying x = 3.298437881

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.701562119, 3.298437881}

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