x^2-17x-25=7x-1

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Solution for x^2-17x-25=7x-1 equation:


Simplifying
x2 + -17x + -25 = 7x + -1

Reorder the terms:
-25 + -17x + x2 = 7x + -1

Reorder the terms:
-25 + -17x + x2 = -1 + 7x

Solving
-25 + -17x + x2 = -1 + 7x

Solving for variable 'x'.

Reorder the terms:
-25 + 1 + -17x + -7x + x2 = -1 + 7x + 1 + -7x

Combine like terms: -25 + 1 = -24
-24 + -17x + -7x + x2 = -1 + 7x + 1 + -7x

Combine like terms: -17x + -7x = -24x
-24 + -24x + x2 = -1 + 7x + 1 + -7x

Reorder the terms:
-24 + -24x + x2 = -1 + 1 + 7x + -7x

Combine like terms: -1 + 1 = 0
-24 + -24x + x2 = 0 + 7x + -7x
-24 + -24x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-24 + -24x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -24x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + -24x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -24x + x2 = 0 + 24
-24x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
-24x + x2 = 24

The x term is -24x.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24x + 144 + x2 = 24 + 144

Reorder the terms:
144 + -24x + x2 = 24 + 144

Combine like terms: 24 + 144 = 168
144 + -24x + x2 = 168

Factor a perfect square on the left side:
(x + -12)(x + -12) = 168

Calculate the square root of the right side: 12.961481397

Break this problem into two subproblems by setting 
(x + -12) equal to 12.961481397 and -12.961481397.

Subproblem 1

x + -12 = 12.961481397 Simplifying x + -12 = 12.961481397 Reorder the terms: -12 + x = 12.961481397 Solving -12 + x = 12.961481397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 12.961481397 + 12 Combine like terms: -12 + 12 = 0 0 + x = 12.961481397 + 12 x = 12.961481397 + 12 Combine like terms: 12.961481397 + 12 = 24.961481397 x = 24.961481397 Simplifying x = 24.961481397

Subproblem 2

x + -12 = -12.961481397 Simplifying x + -12 = -12.961481397 Reorder the terms: -12 + x = -12.961481397 Solving -12 + x = -12.961481397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -12.961481397 + 12 Combine like terms: -12 + 12 = 0 0 + x = -12.961481397 + 12 x = -12.961481397 + 12 Combine like terms: -12.961481397 + 12 = -0.961481397 x = -0.961481397 Simplifying x = -0.961481397

Solution

The solution to the problem is based on the solutions from the subproblems. x = {24.961481397, -0.961481397}

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