x^2+17.4*x-17.4=0

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Solution for x^2+17.4*x-17.4=0 equation:


Simplifying
x2 + 17.4x + -17.4 = 0

Reorder the terms:
-17.4 + 17.4x + x2 = 0

Solving
-17.4 + 17.4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '17.4' to each side of the equation.
-17.4 + 17.4x + 17.4 + x2 = 0 + 17.4

Reorder the terms:
-17.4 + 17.4 + 17.4x + x2 = 0 + 17.4

Combine like terms: -17.4 + 17.4 = 0.0
0.0 + 17.4x + x2 = 0 + 17.4
17.4x + x2 = 0 + 17.4

Combine like terms: 0 + 17.4 = 17.4
17.4x + x2 = 17.4

The x term is 17.4x.  Take half its coefficient (8.7).
Square it (75.69) and add it to both sides.

Add '75.69' to each side of the equation.
17.4x + 75.69 + x2 = 17.4 + 75.69

Reorder the terms:
75.69 + 17.4x + x2 = 17.4 + 75.69

Combine like terms: 17.4 + 75.69 = 93.09
75.69 + 17.4x + x2 = 93.09

Factor a perfect square on the left side:
(x + 8.7)(x + 8.7) = 93.09

Calculate the square root of the right side: 9.648315915

Break this problem into two subproblems by setting 
(x + 8.7) equal to 9.648315915 and -9.648315915.

Subproblem 1

x + 8.7 = 9.648315915 Simplifying x + 8.7 = 9.648315915 Reorder the terms: 8.7 + x = 9.648315915 Solving 8.7 + x = 9.648315915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.7' to each side of the equation. 8.7 + -8.7 + x = 9.648315915 + -8.7 Combine like terms: 8.7 + -8.7 = 0.0 0.0 + x = 9.648315915 + -8.7 x = 9.648315915 + -8.7 Combine like terms: 9.648315915 + -8.7 = 0.948315915 x = 0.948315915 Simplifying x = 0.948315915

Subproblem 2

x + 8.7 = -9.648315915 Simplifying x + 8.7 = -9.648315915 Reorder the terms: 8.7 + x = -9.648315915 Solving 8.7 + x = -9.648315915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.7' to each side of the equation. 8.7 + -8.7 + x = -9.648315915 + -8.7 Combine like terms: 8.7 + -8.7 = 0.0 0.0 + x = -9.648315915 + -8.7 x = -9.648315915 + -8.7 Combine like terms: -9.648315915 + -8.7 = -18.348315915 x = -18.348315915 Simplifying x = -18.348315915

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.948315915, -18.348315915}

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