(-5x*x)-4x+17=0

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Solution for (-5x*x)-4x+17=0 equation:


Simplifying
(-5x * x) + -4x + 17 = 0

Multiply x * x
(-5x2) + -4x + 17 = 0

Reorder the terms:
17 + -4x + (-5x2) = 0

Solving
17 + -4x + (-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 + 0.8x + x2 = 0

Move the constant term to the right:

Add '3.4' to each side of the equation.
-3.4 + 0.8x + 3.4 + x2 = 0 + 3.4

Reorder the terms:
-3.4 + 3.4 + 0.8x + x2 = 0 + 3.4

Combine like terms: -3.4 + 3.4 = 0.0
0.0 + 0.8x + x2 = 0 + 3.4
0.8x + x2 = 0 + 3.4

Combine like terms: 0 + 3.4 = 3.4
0.8x + x2 = 3.4

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = 3.4 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = 3.4 + 0.16

Combine like terms: 3.4 + 0.16 = 3.56
0.16 + 0.8x + x2 = 3.56

Factor a perfect square on the left side:
((x) + 0.4)((x) + 0.4) = 3.56

Calculate the square root of the right side: 1.886796226

Break this problem into two subproblems by setting 
((x) + 0.4) equal to 1.886796226 and -1.886796226.

Subproblem 1

(x) + 0.4 = 1.886796226 Simplifying (x) + 0.4 = 1.886796226 x + 0.4 = 1.886796226 Reorder the terms: 0.4 + x = 1.886796226 Solving 0.4 + x = 1.886796226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 1.886796226 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 1.886796226 + -0.4 x = 1.886796226 + -0.4 Combine like terms: 1.886796226 + -0.4 = 1.486796226 x = 1.486796226 Simplifying x = 1.486796226

Subproblem 2

(x) + 0.4 = -1.886796226 Simplifying (x) + 0.4 = -1.886796226 x + 0.4 = -1.886796226 Reorder the terms: 0.4 + x = -1.886796226 Solving 0.4 + x = -1.886796226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -1.886796226 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -1.886796226 + -0.4 x = -1.886796226 + -0.4 Combine like terms: -1.886796226 + -0.4 = -2.286796226 x = -2.286796226 Simplifying x = -2.286796226

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.486796226, -2.286796226}

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