-5x^2-2x+17=0

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Solution for -5x^2-2x+17=0 equation:


Simplifying
-5x2 + -2x + 17 = 0

Reorder the terms:
17 + -2x + -5x2 = 0

Solving
17 + -2x + -5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-3.4 + 0.4x + x2 = 0

Move the constant term to the right:

Add '3.4' to each side of the equation.
-3.4 + 0.4x + 3.4 + x2 = 0 + 3.4

Reorder the terms:
-3.4 + 3.4 + 0.4x + x2 = 0 + 3.4

Combine like terms: -3.4 + 3.4 = 0.0
0.0 + 0.4x + x2 = 0 + 3.4
0.4x + x2 = 0 + 3.4

Combine like terms: 0 + 3.4 = 3.4
0.4x + x2 = 3.4

The x term is 0.4x.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4x + 0.04 + x2 = 3.4 + 0.04

Reorder the terms:
0.04 + 0.4x + x2 = 3.4 + 0.04

Combine like terms: 3.4 + 0.04 = 3.44
0.04 + 0.4x + x2 = 3.44

Factor a perfect square on the left side:
(x + 0.2)(x + 0.2) = 3.44

Calculate the square root of the right side: 1.854723699

Break this problem into two subproblems by setting 
(x + 0.2) equal to 1.854723699 and -1.854723699.

Subproblem 1

x + 0.2 = 1.854723699 Simplifying x + 0.2 = 1.854723699 Reorder the terms: 0.2 + x = 1.854723699 Solving 0.2 + x = 1.854723699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 1.854723699 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 1.854723699 + -0.2 x = 1.854723699 + -0.2 Combine like terms: 1.854723699 + -0.2 = 1.654723699 x = 1.654723699 Simplifying x = 1.654723699

Subproblem 2

x + 0.2 = -1.854723699 Simplifying x + 0.2 = -1.854723699 Reorder the terms: 0.2 + x = -1.854723699 Solving 0.2 + x = -1.854723699 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -1.854723699 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -1.854723699 + -0.2 x = -1.854723699 + -0.2 Combine like terms: -1.854723699 + -0.2 = -2.054723699 x = -2.054723699 Simplifying x = -2.054723699

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.654723699, -2.054723699}

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